%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.80",
%%%     date            = "07 July 2025",
%%%     time            = "09:14:07 MDT",
%%%     filename        = "marsaglia-george.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     checksum        = "56287 6305 29051 293689",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "random numbers; statistics",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of
%%%                        George Marsaglia (March 12, 1924--February
%%%                        15, 2011), late Professor Emeritus of Pure
%%%                        and Applied Mathematics, Computer Science and
%%%                        Statistics, Washington State and Florida
%%%                        State University (Pullman, WA, USA, and
%%%                        Tallahassee, FL, USA).  The companion LaTeX
%%%                        file marsaglia-george.ltx can be used to
%%%                        typeset this bibliography.
%%%
%%%                        In a trailing section, this bibliography also
%%%                        contains publications that mention
%%%                        Marsaglia's work in their titles.
%%%
%%%                        At version 1.80, the year coverage looked
%%%                        like this:
%%%
%%%                             1948 (   1)    1971 (   2)    1994 (   4)
%%%                             1949 (   0)    1972 (   4)    1995 (   3)
%%%                             1950 (   0)    1973 (   1)    1996 (   1)
%%%                             1951 (   1)    1974 (   4)    1997 (   3)
%%%                             1952 (   1)    1975 (   4)    1998 (   3)
%%%                             1953 (   1)    1976 (   3)    1999 (   2)
%%%                             1954 (   2)    1977 (   1)    2000 (   5)
%%%                             1955 (   0)    1978 (   1)    2001 (   3)
%%%                             1956 (   0)    1979 (   0)    2002 (   2)
%%%                             1957 (   4)    1980 (   2)    2003 (   6)
%%%                             1958 (   0)    1981 (   0)    2004 (   6)
%%%                             1959 (   0)    1982 (   0)    2005 (   5)
%%%                             1960 (   3)    1983 (   4)    2006 (   2)
%%%                             1961 (   6)    1984 (   4)    2007 (   0)
%%%                             1962 (   7)    1985 (   5)    2008 (   0)
%%%                             1963 (   9)    1986 (   1)    2009 (   0)
%%%                             1964 (  14)    1987 (   1)    2010 (   2)
%%%                             1965 (  10)    1988 (   5)    2011 (   5)
%%%                             1966 (   1)    1989 (   5)    2012 (   1)
%%%                             1967 (   8)    1990 (   5)    2013 (   0)
%%%                             1968 (   4)    1991 (   2)    2014 (   1)
%%%                             1969 (   4)    1992 (   4)    2015 (   0)
%%%                             1970 (   5)    1993 (   8)    2016 (   1)
%%%                             19xx (   1)
%%%
%%%                             Article:        117
%%%                             Book:             6
%%%                             InCollection:    11
%%%                             InProceedings:    4
%%%                             MastersThesis:    1
%%%                             Misc:             9
%%%                             PhdThesis:        1
%%%                             Proceedings:     11
%%%                             TechReport:      41
%%%                             Unpublished:      2
%%%
%%%                             Total entries:  203
%%%
%%%                        This file is available as part of the BibNet
%%%                        Project.  The master copy is available for
%%%                        public access on ftp.math.utah.edu in the
%%%                        directory tree /pub/bibnet/authors.  It is
%%%                        mirrored to netlib.bell-labs.com in the
%%%                        directory tree /netlib/bibnet/authors, from
%%%                        which it is available via anonymous ftp and
%%%                        the Netlib service.
%%%
%%%                        This bibliography was prepared from data in
%%%                        the author's personal bibliography files, the
%%%                        TeX User Group bibliography archive, the
%%%                        BibNet Project bibliography archive, the
%%%                        Karlsruhe Computer Science bibliography
%%%                        archive, the University of Trier Digital
%%%                        Bibliography and Library Project archives,
%%%                        the MathSciNet database, the ACM Portal
%%%                        database, the Compendex database, the IEEE
%%%                        Xplore database, the Science Citation Index
%%%                        database, and the ZentralBlatt Math database.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

@Preamble{
    "\input path.sty" #
    "\ifx \undefined \Tan \def \Tan {\hbox{Tan}} \fi"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Institute abbreviations:

@String{inst-BOEING-SRL         = "Boeing Scientific Research Laboratories"}
@String{inst-BOEING-SRL:adr     = "Seattle, WA, USA"}

@String{inst-MATHWORKS          = "The MathWorks, Inc."}
@String{inst-MATHWORKS:adr      = "3 Apple Hill Drive, Natick, MA 01760-2098,
                                  USA"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-ANN-APPL-PROBAB       = "Annals of applied probability"}

@String{j-ANN-MATH-STAT         = "Annals of mathematical statistics"}

@String{j-ANN-PROBAB            = "Annals of Probability"}

@String{j-ANN-STAT              = "Annals of Statistics"}

@String{j-ARS-COMB              = "Ars Combinatoria. The Canadian Journal of
                                  Combinatorics"}

@String{j-BIOMETRIKA            = "Biometrika"}

@String{j-BLOOD                 = "Blood"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CAN-MATH-BULL         = "Canadian mathematical bulletin = Bulletin
                                  canadien de math{\'e}matiques"}

@String{j-J-CLIN-INVEST         = "Journal of Clinical Investigation"}

@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with Applications"}

@String{j-COMPUT-MATH-APPL-B    = "Computers and Mathematics with Applications.
                                  Part B"}

@String{j-COMP-PHYS-COMM        = "Computer Physics Communications"}

@String{j-COMPUT-PHYS           = "Computers in physics"}

@String{j-CRYPTOLOGIA           = "Cryptologia"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INT-J-MOD-PHYS-C      = "International Journal of Modern Physics C [Physics and Computers]"}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-FRANKLIN-INST       = "Journal of the Franklin Institute"}

@String{j-J-LAB-CLIN-MED        = "Journal of Laboratory and Clinical Medicine"}

@String{j-J-MOD-APPL-STAT-METH  = "Journal of Modern Applied Statistical
                                  Methods"}

@String{j-J-R-STAT-SOC-SER-B-METHODOL = "Journal of the Royal Statistical
                                  Society. Series B (Methodological)"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                  Simulation"}

@String{j-J-STAT-SOFT           = "Journal of Statistical Software"}

@String{j-J-SUPERCOMPUTING      = "The Journal of Supercomputing"}

@String{j-LIN-AND-MULT-ALGEBRA  = "Linear and Multilinear Algebra"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MANUSCR-MATH          = "Manuscripta Mathematica"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MEDICINE              = "Medicine (Baltimore)"}

@String{j-METRIKA               = "Metrika. International Journal for
                                  Theoretical and Applied Statistics."}

@String{j-MONTE-CARLO-METHODS-APPL = "Monte Carlo Methods and Applications"}

@String{j-NEW-ENGLAND-J-MED     = "The New England Journal of Medicine"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-OPER-RES              = "Operations Research"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PHYS-REV-LET          = "Physical Review Letters"}

@String{j-PLANET-SPACE-SCI      = "Planetary and Space Science"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
                                  Sciences of the United States of America"}

@String{j-RADIAT-RES            = "Radiation Research"}

@String{j-SANKHYA-A             = "Sankhy{\={a}} (Indian Journal of
                                  Statistics), Series A. Methods and
                                  Techniques"}

@String{j-SCIENCE-NEWS          = "Science News (Washington, DC)"}

@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM Journal on Scientific and Statistical
                                  Computing"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGADA-LETTERS        = "ACM SIGADA Ada Letters"}

@String{j-SIGPLAN               = "ACM SIG{\-}PLAN Notices"}

@String{j-STAT-NEERLANDICA      = "Statistica Neerlandica. Journal of the
                                  Netherlands Society for Statistics and
                                  Operations Research"}

@String{j-STAT-PROB-LETT        = "Statistics \& Probability Letters"}

@String{j-TECHNOMETRICS         = "Technometrics"}

@String{j-TOMACS                = "ACM Transactions on Modeling and Computer
                                  Simulation"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-TRANSFUSION           = "Transfusion"}

%%% ====================================================================
%%% Publishers and their addresses:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-ELS                 = "Elsevier Science Publishers B.V."}
@String{pub-ELS:adr             = "Amsterdam, The Netherlands"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                   Spring, MD 20910, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-VAN-NOSTRAND-REINHOLD = "Van Nostrand Reinhold"}
@String{pub-VAN-NOSTRAND-REINHOLD:adr = "New York, NY, USA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

%%% ====================================================================
%%% Bibliography entries, sort by year and citation label:

@MastersThesis{Marsaglia:1948:SSP,
  author =       "George Marsaglia",
  title =        "The structures of stochastic processes",
  type =         "Thesis ({M.A.})",
  school =       "The Ohio State University",
  address =      "Columbus, OH, USA",
  pages =        "??",
  year =         "1948",
  bibdate =      "Wed Jun 22 07:15:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Marsaglia:1951:SPC,
  author =       "George Marsaglia",
  title =        "Stochastic Processes and Classes of Random Variables",
  type =         "{Ph.D.} thesis",
  school =       "The Ohio State University",
  address =      "Columbus, OH, USA",
  pages =        "46",
  year =         "1951",
  bibdate =      "Wed Jun 22 07:10:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://ezproxy.lib.utah.edu/docview/302068737?accountid=14677",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1953:NCD,
  author =       "George Marsaglia",
  title =        "A Note on the Compatibility of Distribution
                 Functions",
  type =         "Report",
  number =       "85",
  institution =  "Institute of Statistics, University of North
                 Carolina",
  address =      "Chapel Hill, NC, USA",
  pages =        "ii + 2",
  day =          "12",
  month =        nov,
  year =         "1953",
  bibdate =      "Tue Jun 21 19:20:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/get-tr-doc/pdf?AD=AD0029405",
  acknowledgement = ack-nhfb,
  remark =       "Special report to the Office of Naval Research of work
                 at Chapel Hill under Project NR 042 031, Contract
                 N7-onr-28492, for research in probability and
                 statistics.",
}

@TechReport{Marsaglia:1954:ILCa,
  author =       "George Marsaglia",
  title =        "Iterated limits and the central limit theorem for
                 dependent variables",
  type =         "Special Report",
  number =       "93",
  institution =  "Institute of Statistics, University of North
                 Carolina",
  address =      "Chapel Hill, NC, USA",
  pages =        "ii + 7",
  month =        feb,
  year =         "1954",
  bibdate =      "Wed Nov 12 07:27:27 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0035146;
                 http://www.dtic.mil/dtic/tr/fulltext/u2/035146.pdf;
                 http://www.dtic.mil/get-tr-doc/pdf?AD=AD0035146",
  acknowledgement = ack-nhfb,
  remark =       "Special report to the Office of Naval Research of work
                 at Chapel Hill under Project NR 042 031 for research in
                 probability and statistics.",
}

@Article{Marsaglia:1954:ILCb,
  author =       "George Marsaglia",
  title =        "Iterated limits and the central limit theorem for
                 dependent variables",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "5",
  number =       "6",
  pages =        "987--991",
  month =        dec,
  year =         "1954",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "60.0X",
  MRnumber =     "16,494e",
  MRreviewer =   "D. G. Kendall",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database; ZentralBlatt Math database",
  ZMnumber =     "0056.36102",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  keywords =     "Probability theory",
}

@Article{Graybill:1957:IMQ,
  author =       "Franklin A. Graybill and George Marsaglia",
  title =        "Idempotent matrices and quadratic forms in the general
                 linear hypothesis",
  journal =      j-ANN-MATH-STAT,
  volume =       "28",
  number =       "3",
  pages =        "678--686",
  month =        sep,
  year =         "1957",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177706879",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "62.0X",
  MRnumber =     "19,1095e",
  MRreviewer =   "M. Dwass",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aoms/1177706879",
  ZMnumber =     "0080.35502",
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "Statistics",
  ZMreviewer =   "T. V. Narayana",
}

@TechReport{Marsaglia:1957:GLH,
  author =       "George Marsaglia",
  title =        "The General Linear Hypothesis",
  type =         "Statistical paper",
  number =       "2",
  institution =  "Departments of Economics, Statistics \& Commerce,
                 University of Rangoon",
  address =      "Rangoon, Burma",
  month =        "????",
  year =         "1957",
  bibdate =      "Wed Jun 22 06:56:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.worldcat.org/title/general-linear-hypothesis/oclc/27397695",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1957:NCM,
  author =       "George Marsaglia",
  title =        "A note on the construction of a multivariate normal
                 sample",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "3",
  number =       "2",
  pages =        "149--149",
  month =        jun,
  year =         "1957",
  CODEN =        "IETTAW",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Thu Aug 05 08:58:22 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "This note points out the superfluity of a method of
                 Stein and Storer for constructing a multivariate normal
                 sample, and suggests a simple alternative.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@TechReport{Marsaglia:1960:GED,
  author =       "George Marsaglia",
  title =        "On generating exponentially distributed random
                 variables",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        "????",
  year =         "1960",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1960:TDQ,
  author =       "George Marsaglia",
  title =        "Tables of the distribution of quadratic forms of ranks
                 two and three",
  type =         "Report",
  number =       "213",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        "????",
  year =         "1960",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1960:TSR,
  author =       "George Marsaglia",
  title =        "Tables of {$ 1 / 2 \pi {\Tan }^{-1}(\lambda) $} and {$
                 {\Tan }^{-1}(\lambda) $} for $ \lambda = .0001, .0002,
                 \ldots {}, .9999 $, with some remarks on their use in
                 finding the normal probability measure of polygonal
                 regions",
  type =         "Report",
  number =       "D1-82-0078",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        "????",
  year =         "1960",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1961:ERV,
  author =       "G. Marsaglia",
  title =        "Expressing a random variable in terms of uniform
                 random variables",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "3",
  pages =        "894--898",
  month =        sep,
  year =         "1961",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177704983",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65.15",
  MRnumber =     "23 \#B3122",
  MRreviewer =   "M. E. Muller",
  bibdate =      "Thu Dec 22 07:41:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aoms/1177704983;
                 http://www.jstor.org/stable/2237849",
  ZMnumber =     "0139.35604",
  abstract =     "This note suggests that expressing a distribution
                 function as a mixture of suitably chosen distribution
                 functions leads to improved methods for generating
                 random variables in a computer. The idea is to choose a
                 distribution function which is close to the original
                 and use it most of the time, applying the correction
                 only infrequently. Mixtures allow this to be done in
                 probability terms rather than in the more elaborate
                 ways of conventional numerical analysis, which must be
                 applied every time.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  HDnumber =     "75",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "probability theory",
}

@Article{Marsaglia:1961:GER,
  author =       "G. Marsaglia",
  title =        "Generating exponential random variables",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "3",
  pages =        "899--900",
  month =        sep,
  year =         "1961",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177704984",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65.15",
  MRnumber =     "23 \#B3123",
  MRreviewer =   "M. E. Muller",
  bibdate =      "Thu Dec 22 07:41:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aoms/1177704984;
                 http://www.jstor.org/stable/2237850",
  ZMnumber =     "0139.35603",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  HDnumber =     "76",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "probability theory",
}

@TechReport{Marsaglia:1961:PGN,
  author =       "George Marsaglia",
  title =        "Procedures for Generating Normal Random Variables,
                 {II}",
  type =         "Mathematical note",
  number =       "243",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        oct,
  year =         "1961",
  bibdate =      "Tue Jun 21 18:56:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "A method for generating a normal random variable in
                 terms of uniform random variables is described. The
                 method is based on representing a density function as a
                 mixture of simpler densities. It is fast and requires
                 little storage (60 constants). It is not quite as fast
                 as other methods, but it is simpler, with less chance
                 for prospective users being set adrift in a sea of
                 details",
  acknowledgement = ack-nhfb,
  HDnumber =     "78",
}

@TechReport{Marsaglia:1961:RGR,
  author =       "G. Marsaglia",
  title =        "Remark on generating a random variable having a nearly
                 linear density function",
  type =         "Mathematical Note",
  number =       "242",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  year =         "1961",
  bibdate =      "Mon Jun 27 15:17:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  HDnumber =     "77",
}

@Article{Marsaglia:1961:SPT,
  author =       "George Marsaglia",
  title =        "Some probability theory associated with
                 clustered-rocket flights",
  journal =      j-PLANET-SPACE-SCI,
  volume =       "4",
  number =       "??",
  pages =        "194--201",
  month =        jan,
  year =         "1961",
  CODEN =        "PLSSAE",
  DOI =          "https://doi.org/10.1016/0032-0633(61)90132-5",
  ISSN =         "0032-0633 (print), 1873-5088 (electronic)",
  ISSN-L =       "0032-0633",
  bibdate =      "Wed Jun 22 06:45:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0032063361901325",
  abstract =     "The primary purpose of this note is to provide the
                 probability distribution of the amount of propellant
                 remaining in a cluster of rocket engines at the times
                 that the first and second burnouts occur. In addition,
                 various other random variables associated with the
                 random behavior of the engines of a cluster (pitch and
                 yaw moments, time between successive burnouts, etc.)
                 are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Planetary and Space Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00320633",
}

@TechReport{Marsaglia:1961:UDS,
  author =       "George Marsaglia",
  title =        "Uniform Distributions Over a Simplex",
  type =         "Mathematical note",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        dec,
  year =         "1961",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hosain:1962:NII,
  author =       "F. Hosain and G. Marsaglia and W. Noyes and C. A.
                 Finch",
  title =        "The nature of internal iron exchange in man",
  journal =      "Transactions of the Association of American
                 Physicians",
  volume =       "75",
  number =       "??",
  pages =        "59--63",
  month =        "????",
  year =         "1962",
  ISSN =         "0066-9458",
  bibdate =      "Mon Jun 3 19:13:11 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the Association of American
                 Physicians",
}

@TechReport{Mann:1962:RC,
  author =       "H. B. Mann and G. Marsaglia",
  title =        "A Remark on Circulants",
  type =         "Mathematical note",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        "????",
  year =         "1962",
  bibdate =      "Wed Jun 22 06:43:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1962:ERB,
  author =       "George Marsaglia",
  title =        "Elementary Relations Between Uniform and Normal
                 Distributions in the Plane",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        aug,
  year =         "1962",
  bibdate =      "Wed Nov 12 07:29:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0288501",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1962:FPG,
  author =       "G. Marsaglia and M. D. Maclaren and T. A. Bray",
  title =        "A Fast Procedure for Generating Normal Random
                 Variables",
  type =         "Mathematical note",
  number =       "282",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        aug,
  year =         "1962",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=AD0296195",
  abstract =     "A discussion is given of the generation of normal
                 random variables very rapidly in a computer --- for
                 example, at the rate of 10,000--15,000 per second in
                 the IBM 7090. The method is suitable for any computer.
                 The incorporation of successive improvements has led to
                 a procedure which is fairly easy to program, requires
                 little storage, 300--400 constants, is very fast (it
                 takes about as long to generate the normal $x$ as the
                 uniform $u$ from which it comes), and is completely
                 accurate, in the sense that in theory the procedure
                 returns a random variable with exactly the required
                 distribution; in practice the result is an
                 approximation influenced only by the capacity (word
                 length) of the computer.",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1962:IPM,
  author =       "George Marsaglia",
  title =        "Improving the Polar Method for Generating a Pair of
                 Normal Random Variables",
  type =         "Technical report",
  number =       "D1-82-0203",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        sep,
  year =         "1962",
  bibdate =      "Wed Nov 12 07:34:34 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0288931",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1962:RVC,
  author =       "George Marsaglia",
  title =        "Random Variables and Computers",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        may,
  year =         "1962",
  bibdate =      "Wed Nov 12 07:29:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0278358",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1962:SPG,
  author =       "George Marsaglia and T. A. Bray",
  title =        "A small procedure for generating normal random
                 variables",
  type =         "Mathematical note",
  number =       "283",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        nov,
  year =         "1962",
  bibdate =      "Wed Jun 22 09:24:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{MacLaren:1963:FPG,
  author =       "M. D. MacLaren and G. Marsaglia and T. A. Bray",
  title =        "A Fast Procedure for Generating Exponential Random
                 Variables",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        jan,
  year =         "1963",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "A very fast method for generating exponential random
                 variables in a digital computer is presented. The
                 method is exact, in the sense that in theory it returns
                 a random variable with exactly the exponential
                 distribution. In practice the result is an
                 approximation, but the accuracy of the approximation
                 depends only on the word length of the computer.",
  acknowledgement = ack-nhfb,
  remark =       "Published in \cite{MacLaren:1964:FPG}.",
}

@TechReport{Marsaglia:1963:CER,
  author =       "George Marsaglia",
  title =        "The Cumulative Effect of Random Losses in a
                 Transmission Line",
  type =         "Mathematical note",
  number =       "D1-82-0236",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "ii + 14",
  month =        feb,
  year =         "1963",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "Mathematical Note number 289.",
  URL =          "http://www.dtic.mil/docs/citations/AD0403722;
                 http://www.dtic.mil/get-tr-doc/pdf?AD=AD0403722",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1963:CMC,
  author =       "George Marsaglia",
  title =        "Conditional Means and Covariances of Normal Variables
                 with Singular Covariance Matrix",
  type =         "Mathematical note",
  number =       "288",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        feb,
  year =         "1963",
  bibdate =      "Tue Jun 21 18:17:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0299080",
  acknowledgement = ack-nhfb,
  remark =       "Published in \cite{Marsaglia:1964:CMC}.",
}

@TechReport{Marsaglia:1963:ENDa,
  author =       "George Marsaglia",
  title =        "Expressing the Normal Distribution with Covariance
                 Matrix {$ A + B $} in Terms of One with Covariance
                 Matrix {$A$}",
  type =         "Mathematical note",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        feb,
  year =         "1963",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0299120",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1963:ENDb,
  author =       "George Marsaglia",
  title =        "Expressing the Normal Distribution with Covariance
                 Matrix {$ A + B $} in Terms of One with Covariance
                 Matrix {$A$}",
  journal =      j-BIOMETRIKA,
  volume =       "50",
  number =       "3/4",
  pages =        "535--538",
  month =        dec,
  year =         "1963",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2333924",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62.40",
  MRnumber =     "0181061 (31 \#5290)",
  MRreviewer =   "I. Olkin",
  bibdate =      "Sat Jun 21 14:33:13 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315448;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
  URL =          "http://www.jstor.org/stable/2333924",
  ZMnumber =     "0117.37202",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
  keywords =     "statistics",
}

@Article{Marsaglia:1963:GDR,
  author =       "G. Marsaglia",
  title =        "Generating discrete random variables in a computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "1",
  pages =        "37--38",
  month =        jan,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0112.08402",
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7628",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "numerical analysis",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@TechReport{Marsaglia:1963:GVT,
  author =       "George Marsaglia",
  title =        "Generating variables from the tail of the normal
                 distribution",
  type =         "Report",
  number =       "0399324",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "6",
  month =        sep,
  year =         "1963",
  bibdate =      "Wed Jun 22 09:12:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0423993;
                 http://www.stormingmedia.us/39/3993/0399324.html",
  acknowledgement = ack-nhfb,
  xxtitle =      "Generating a Variable from the Tail of the Normal
                 Distribution",
}

@TechReport{Marsaglia:1963:RNF,
  author =       "George Marsaglia",
  title =        "Random numbers fall mainly in the planes",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "9",
  month =        aug,
  year =         "1963",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0685578",
  abstract =     "Most of the world's computer centers use congruential
                 random number generators. This note points out that
                 such random number generators produce points in $ 2, 3,
                 4, \ldots {} $ dimensions which are too regular for
                 many Monte Carlo calculations. The trouble is that the
                 points fall exactly on a lattice with quite a gross
                 structure. The paper gives details of the degree of
                 regularity of such generators in terms of sets of
                 relatively few parallel hyperplanes which contain all
                 of the points produced by the generator.",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1963:SAM,
  author =       "George Marsaglia",
  title =        "Stochastic Analysis of Multi-Compartment Systems",
  type =         "Mathematical note",
  number =       "313",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "22",
  month =        jul,
  year =         "1963",
  bibdate =      "Tue Jun 21 18:14:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "This is a discussion of methods for describing,
                 mathematically, flows between compartments in a
                 multi-compartment system. We will give the conventional
                 theory, based on the solution of a system of linear
                 differential equations; we will also give a theory
                 based on probability, viewing the system as a
                 collection of `states' with a particle moving from
                 state to state with certain probabilities, remaining in
                 each state a random time with an exponential
                 distribution. Finally, we will take still another
                 approach, again based on probability theory, in which
                 we consider the sojourn time of a particle, that is,
                 the time it spends after leaving a given compartment
                 before returning to that compartment.",
  acknowledgement = ack-nhfb,
}

@Article{MacLaren:1964:FPG,
  author =       "M. D. MacLaren and G. Marsaglia and T. A. Bray",
  title =        "A fast procedure for generating exponential random
                 variables",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "298--300",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
  ZMnumber =     "0127.09101",
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7614",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "numerical analysis; PRNG (pseudo-random number
                 generator)",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@TechReport{Marsaglia:1964:BRS,
  author =       "George Marsaglia",
  title =        "Bounds for the Rank of the Sum of Two Matrices",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "13",
  month =        apr,
  year =         "1964",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0600471",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1964:CMC,
  author =       "George Marsaglia",
  title =        "Conditional Means and Covariances of Normal Variables
                 with Singular Covariance Matrix",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "59",
  number =       "308",
  pages =        "1203--1204",
  month =        dec,
  year =         "1964",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:37 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314189;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib",
  URL =          "http://www.jstor.org/stable/2282635",
  ZMnumber =     "0124.11303",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "statistics",
}

@Article{Marsaglia:1964:CMG,
  author =       "G. Marsaglia and T. A. Bray",
  title =        "A Convenient Method for Generating Normal Variables",
  journal =      j-SIAM-REVIEW,
  volume =       "6",
  number =       "3",
  pages =        "260--264",
  month =        "????",
  year =         "1964",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1006063",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65.15",
  MRnumber =     "30 \#2660",
  MRreviewer =   "D. H. Lehmer",
  bibdate =      "Thu Mar 27 09:05:15 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/6/3;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2027592",
  ZMnumber =     "0125.08001",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1964",
}

@Article{Marsaglia:1964:FPG,
  author =       "G. Marsaglia and M. D. MacLaren and T. A. Bray",
  title =        "A fast procedure for generating normal random
                 variables",
  journal =      j-CACM,
  volume =       "7",
  number =       "1",
  pages =        "4--10",
  month =        jan,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363872.363883",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:51 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  ZMnumber =     "0127.09005",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7637",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "numerical analysis; PRNG (pseudo-random number
                 generator)",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@Article{Marsaglia:1964:GVT,
  author =       "George Marsaglia",
  title =        "Generating a Variable from the Tail of the Normal
                 Distribution",
  journal =      j-TECHNOMETRICS,
  volume =       "6",
  number =       "1",
  pages =        "101--102",
  month =        feb,
  year =         "1964",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Wed Jun 22 09:29:50 2011",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstor.org/stable/1266749",
  acknowledgement = ack-nhfb,
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7629",
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html;
                 http://www.tandfonline.com/loi/utch20",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@TechReport{Marsaglia:1964:MCR,
  author =       "George Marsaglia and Albert W. Marshall and Frank
                 Proschan",
  title =        "Moment Crossings as Related to Density Crossings",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "??",
  month =        jul,
  year =         "1964",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0603582",
  abstract =     "In this paper it is shown how the number of moment
                 crossings of two symmetrical densities is related to
                 the number of crossings of the densities. This
                 generalizes a result of Fisher's recently proved by
                 Finucan (1964) (A note on Kurtosis).",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1964:MPR,
  author =       "George Marsaglia",
  title =        "A Method for Producing Random Variables in a
                 Computer",
  type =         "Mathematical note",
  number =       "342",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "13",
  month =        feb,
  year =         "1964",
  bibdate =      "Tue Jun 21 18:14:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0601118",
  abstract =     "This paper describes a general procedure for producing
                 random variables in a computer. The idea is to
                 represent the required $X$ in the form: $ X = C (M +
                 U_1 + U_2 + U_3) $, some 97--99\% of the time, where c
                 is constant, $M$ is a discrete random variable taking
                 perhaps $8$ values, and the $U$'s are uniform random
                 variables; the other 1--3\% of the time, $X$ is
                 generated from a residual density by the rejection
                 technique. These two methods for producing $X$ are
                 combined in the proper proportions in order that the
                 resulting distribution for $X$ be correct. The method
                 is general in that it applies to a wide variety of
                 density functions. Programs based on this procedure are
                 very fast and require little computer storage space ---
                 typically, 18 constants and 20 instructions.",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1964:RDA,
  author =       "George Marsaglia",
  title =        "The Radiation Dose Accumulated by Blood Diverted
                 Through a Shunt",
  type =         "Mathematical note",
  number =       "357",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "8",
  month =        jul,
  year =         "1964",
  bibdate =      "Tue Jun 21 19:32:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "Modern techniques have made it possible to divert a
                 portion of the circulating blood through a shunt
                 outside the body --- for example in heart-lung
                 machines, artificial kidneys, and coiled tubes where
                 the blood may be exposed to radiation without danger to
                 body tissues. There is some probability theory
                 connected with such procedures, for the cells of the
                 blood are thoroughly mixed in the body, and hence the
                 number of times a blood cell passes through the shunt
                 is a random variable. Several papers have been written
                 to describe such systems by differential equations;
                 this paper discusses the problem directly in terms of
                 probability theory, finding the exact distribution of
                 the number of times a blood cell has passed through the
                 shunt and, in addition, a normal approximation which
                 makes calculation of accumulated doses a matter of
                 simple arithmetic.",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1964:RNV,
  author =       "George Marsaglia",
  title =        "Ratios of normal variables and ratios of sums of
                 variables",
  type =         "Mathematical note",
  number =       "D1-82-0348",
  institution =  "Mathematics Research Laboratory, Boeing Scientific
                 Research Laboratories",
  address =      "Seattle, WA, USA",
  pages =        "iii + 13 + 3",
  month =        apr,
  year =         "1964",
  bibdate =      "Wed Nov 12 07:14:08 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0600972;
                 http://www.dtic.mil/dtic/tr/fulltext/u2/600972.pdf;
                 http://www.dtic.mil/get-tr-doc/pdf?AD=AD0600972",
  abstract =     "The principal part of this paper is devoted to the
                 study of the distribution and density functions of the
                 ratio of two normal random variables. It gives several
                 representations of the distribution function in terms
                 of the bivariate normal distribution and Nicholson's
                 $V$ function, both of which have been extensively
                 studied, and for which tables and computational
                 procedures are readily available. One of these
                 representations leads to an easy derivation of the
                 density function in terms of the Cauchy density and the
                 normal density and integral. A number of graphs of the
                 possible shapes of the density are given, together with
                 an indication of when the density is unimodal or
                 bimodal.\par

                 The last part of the paper discusses the distribution
                 of the ratio $ (u_1 + \cdots + u_n) / (v_1 + \cdots +
                 v_m)$ where the $u$'s and $v$'s are, independent,
                 uniform variables. The distribution for all $n$ and $m$
                 is given, and some approximations discussed.",
  acknowledgement = ack-nhfb,
  remark =       "Published in \cite{Marsaglia:1965:RNV}.",
}

@InCollection{Marsaglia:1964:RVC,
  author =       "George Marsaglia",
  title =        "Random variables and computers",
  crossref =     "Kozesnik:1964:TTP",
  pages =        "499--512",
  year =         "1964",
  MRclass =      "65.05 (65.15)",
  MRnumber =     "29 \#1721",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0123.36205",
  keywords =     "probability theory",
}

@TechReport{Marsaglia:1964:SPIa,
  author =       "George Marsaglia",
  title =        "Some Problems Involving Circular and Spherical
                 Targets",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "19",
  month =        apr,
  year =         "1964",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0600566",
  abstract =     "This article is concerned with some problems which
                 occur in certain tactical considerations: how should
                 one place $k$ circles (spheres) in the plane (3-space)
                 so that their union has the greatest standard normal
                 probability measure, that is, so as to maximize the
                 probability that a random normal point will fall in one
                 or more of the circles (spheres). For $ k > 3$ the
                 problem seems hopeless, (except for certain special
                 situations); the case for $ k = 3$ is still unresolved
                 and is being worked on by a number of investigators,
                 and the case for $ k = 2$ is solved completely in this
                 paper. The results for $ k = 2$ have some practical
                 value when applied to actual problems arising in
                 tactical considerations, and some theoretical value, as
                 a method of attacking the problem for $ k > 3$.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1964:SPIb,
  author =       "George Marsaglia",
  title =        "Some Problems Involving Circular and Spherical
                 Targets",
  journal =      j-OPER-RES,
  volume =       "13",
  number =       "1",
  pages =        "18--27",
  month =        jan # "\slash " # feb,
  year =         "1964",
  CODEN =        "OPREAI",
  DOI =          "https://doi.org/10.1287/opre.13.1.18",
  ISSN =         "0030-364X (print), 1526-5463 (electronic)",
  ISSN-L =       "0030-364X",
  bibdate =      "Tue Jun 21 18:50:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.jstor.org/stable/167951",
  abstract =     "This article is concerned with some problems that
                 occur in certain tactical considerations: how should
                 one place $k$ circles [spheres] in the plane [3-space]
                 so that their union has the greatest standard normal
                 probability measure, that is, so as to maximize the
                 probability that a random normal point will fall in one
                 or more of the circles [spheres]. For $ k > 3 $ the
                 problem seems hopeless, (except for certain special
                 situations); the case for $ k = 3 $ is still unresolved
                 and is being worked on by a number of investigators,
                 and the case for $ k = 2 $ is solved completely in this
                 paper. The results for $ k = 2 $ have some practical
                 value when applied to actual problems arising in
                 tactical considerations, and some theoretical value, as
                 a method of attacking the problem for $ k \geq 3 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Operations Research",
  journal-URL =  "http://pubsonline.informs.org/loi/opre",
}

@Article{MacLaren:1965:URN,
  author =       "M. Donald MacLaren and George Marsaglia",
  title =        "Uniform Random Number Generators",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "1",
  pages =        "83--89",
  month =        jan,
  year =         "1965",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321250.321257",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.15",
  MRnumber =     "30 \#687",
  bibdate =      "Mon Jan 22 17:05:44 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib;
                 MathSciNet database",
  ZMnumber =     "0143.40101",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "numerical analysis",
  oldlabel =     "MacLarenM65",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/jacm/MacLarenM65",
}

@Article{Marsaglia:1965:CER,
  author =       "G. Marsaglia",
  title =        "The cumulative effect of random losses in a
                 transmission line",
  journal =      j-J-FRANKLIN-INST,
  volume =       "280",
  number =       "5",
  pages =        "443--450",
  month =        nov,
  year =         "1965",
  CODEN =        "JFINAB",
  DOI =          "https://doi.org/10.1016/0016-0032(65)90533-8",
  ISSN =         "0016-0032 (print), 1879-2693 (electronic)",
  ISSN-L =       "0016-0032",
  bibdate =      "Wed Nov 12 14:50:37 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0173.21401",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of {The Franklin Institute}",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00160032",
  keywords =     "information, communication",
}

@Article{Marsaglia:1965:CNS,
  author =       "George Marsaglia",
  title =        "Classroom Notes: Short Proof of a Result on
                 Determinants",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "72",
  number =       "2",
  pages =        "173--173",
  month =        feb,
  year =         "1965",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Thu Jul 8 18:23:41 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Marsaglia:1965:DRD,
  author =       "G. Marsaglia and E. D. Thomas",
  title =        "Distribution of radiation dose accumulated by blood
                 during extracorporeal irradiation",
  journal =      j-RADIAT-RES,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "1965",
  CODEN =        "RAREAE",
  ISSN =         "0033-7587 (print), 1938-5404 (electronic)",
  ISSN-L =       "0033-7587",
  bibdate =      "Wed Jun 22 08:14:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Radiation Research",
  journal-URL =  "http://www.jstor.org/journal/radirese",
  remark =       "Cited as in press in \cite{Thomas:1965:TLE}.",
}

@Article{Marsaglia:1965:MCR,
  author =       "G. Marsaglia and A. W. Marshall and F. Proschan",
  title =        "Moment crossings as related to density crossings",
  journal =      j-J-R-STAT-SOC-SER-B-METHODOL,
  volume =       "27",
  number =       "1",
  pages =        "91--93",
  month =        jan,
  year =         "1965",
  CODEN =        "JSTBAJ",
  ISSN =         "0035-9246",
  MRclass =      "60.20",
  MRnumber =     "32 \#6514",
  MRreviewer =   "D. R. Barr",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0128.38905",
  fjournal =     "Journal of the Royal Statistical Society. Series B
                 (Methodological)",
  journal-URL =  "http://www.jstor.org/journals/00359246.html",
  keywords =     "statistics",
}

@Article{Marsaglia:1965:RDA,
  author =       "George Marsaglia and E. Donnall Thomas",
  title =        "The Radiation Dose Accumulated by Blood during
                 Extracorporeal Irradiation",
  journal =      j-RADIAT-RES,
  volume =       "25",
  number =       "2",
  pages =        "269--276",
  month =        jun,
  year =         "1965",
  CODEN =        "RAREAE",
  DOI =          "https://doi.org/10.2307/3571970",
  ISSN =         "0033-7587 (print), 1938-5404 (electronic)",
  ISSN-L =       "0033-7587",
  bibdate =      "Tue Jun 21 18:30:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstor.org/stable/3571970",
  acknowledgement = ack-nhfb,
  ajournal =     "Radiat. Res.",
  fjournal =     "Radiation Research",
  journal-URL =  "http://www.jstor.org/journal/radirese",
}

@Article{Marsaglia:1965:RNV,
  author =       "George Marsaglia",
  title =        "Ratios of normal variables and ratios of sums of
                 uniform variables",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "60",
  number =       "309",
  pages =        "193--204",
  month =        mar,
  year =         "1965",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "60.20",
  MRnumber =     "31 \#2747",
  MRreviewer =   "S. R. Searle",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  URL =          "http://www.jstor.org/stable/2283145",
  ZMnumber =     "0126.35302",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "statistics",
}

@TechReport{Marsaglia:1965:SAM,
  author =       "George Marsaglia",
  title =        "Still Another Method for Producing Normal Variables in
                 a Computer",
  type =         "Mathematical note",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "8",
  month =        jan,
  year =         "1965",
  bibdate =      "Tue Jun 21 18:58:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0612430",
  abstract =     "A method for producing normal random variables in
                 terms of uniform random variables $ U_1, U_2, U_3,
                 \ldots {} $. If $ Y = U_1 + U_2 + U_3 $, then choosing
                 one of the four random variables $ 2 Y - 3 $, $ (4 Y -
                 6) / 3 $, $ (Y - 7) / 2 $ or $ (Y + 4) / 2 $ in the
                 proportions $ 0.8365 $, $ 0.11506 $, $ 0.00372 $ and $
                 0.00372 $ will produce the required normal variate $
                 98.6 $ percent of the time. The other $ 1.4 $ percent
                 is devoted to the tail or a rejection technique in
                 order that the composite be exact. The method leads to
                 very fast computer programs which are easy to code and
                 occupy little space in the computer.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1965:SPI,
  author =       "George Marsaglia",
  title =        "Some Problems Involving Circular and Spherical
                 Targets",
  journal =      j-OPER-RES,
  volume =       "13",
  number =       "1",
  pages =        "18--27",
  month =        jan # "\slash " # feb,
  year =         "1965",
  CODEN =        "OPREAI",
  DOI =          "https://doi.org/10.1287/opre.13.1.18",
  ISSN =         "0030-364X (print), 1526-5463 (electronic)",
  ISSN-L =       "0030-364X",
  bibdate =      "Wed Nov 12 10:07:25 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://pubsonline.informs.org/doi/pdf/10.1287/opre.13.1.18",
  acknowledgement = ack-nhfb,
  fjournal =     "Operations Research",
  journal-URL =  "http://pubsonline.informs.org/loi/opre",
}

@Article{Thomas:1965:TLE,
  author =       "E. D. Thomas and R. B. Epstein and J. W. {Eschbach
                 Jr.} and D. Prager and C. D. Buckner and G. Marsaglia",
  title =        "Treatment of Leukemia by Extracorporeal Irradiation",
  journal =      j-NEW-ENGLAND-J-MED,
  volume =       "273",
  number =       "1",
  pages =        "6--12",
  day =          "1",
  month =        jul,
  year =         "1965",
  CODEN =        "NEJMAG",
  DOI =          "https://doi.org/10.1056/NEJM196507012730102",
  ISSN =         "0028-4793 (print), 1533-4406 (electronic)",
  ISSN-L =       "0028-4793",
  bibdate =      "Tue Jun 21 18:20:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pubmed/14297099;
                 http://www.nejm.org/doi/full/10.1056/NEJM196507012730102",
  acknowledgement = ack-nhfb,
  ajournal =     "N. Engl. J. Med.",
  fjournal =     "The New England Journal of Medicine",
  journal-URL =  "http://www.nejm.org/medical-index",
}

@InProceedings{Marsaglia:1966:GMP,
  author =       "G. Marsaglia",
  booktitle =    "Proceedings of the Fall Joint Computer Conference, San
                 Francisco, November 1966",
  title =        "A general method for producing random variables in a
                 computer",
  publisher =    "Spartan Books",
  address =      "Washington, DC, USA",
  bookpages =    "vii + 819",
  pages =        "169--173",
  year =         "1966",
  LCCN =         "TK7885.A1 J74 1966 Fall",
  bibdate =      "Fri Jan 6 09:58:50 2012",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7631",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
  town =         "San Francisco",
}

@Article{Hosain:1967:BFN,
  author =       "Fazle Hosain and George Marsaglia and Clement A.
                 Finch",
  title =        "Blood Ferrokinetics in Normal Man",
  journal =      j-J-CLIN-INVEST,
  volume =       "46",
  number =       "1",
  pages =        "1--9",
  month =        jan,
  year =         "1967",
  CODEN =        "JCINAO",
  DOI =          "https://doi.org/10.1172/JCI105501",
  ISSN =         "0021-9738 (print), 1558-8238 (electronic)",
  ISSN-L =       "0021-9738",
  bibdate =      "Tue Jun 21 18:09:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC297014/",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Clin. Invest.",
  fjournal =     "Journal of Clinical Investigation",
  journal-URL =  "http://www.jci.org/archive",
}

@InCollection{Marsaglia:1967:BRS,
  author =       "George Marsaglia",
  title =        "Bounds on the rank of the sum of matrices",
  crossref =     "Kozesnik:1967:TFP",
  pages =        "455--462",
  year =         "1967",
  MRclass =      "15.05",
  MRnumber =     "36 \#1458",
  MRreviewer =   "C. G. Cullen",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
}

@TechReport{Marsaglia:1967:ORF,
  author =       "George Marsaglia",
  title =        "Optimal Representation of a Function as a Linear
                 Combination of Functions",
  type =         "Report",
  number =       "0841156",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "14",
  month =        mar,
  year =         "1967",
  bibdate =      "Wed Jun 22 06:38:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0651148;
                 http://www.stormingmedia.us/84/8411/0841156.html",
  abstract =     "This paper discusses the approximation of a given
                 density function g(x) with a linear combination of
                 densities $ f_1 (x), f_2 (x), \ldots {}, f_n(x) $ in
                 such a way that the approximation has maximum area but
                 always lies below the given function.",
  acknowledgement = ack-nhfb,
}

@Article{Morgan:1967:MII,
  author =       "E. H. Morgan and G. Marsaglia and E. R. Giblett and C.
                 A. Finch",
  title =        "A method of investigating internal iron exchange
                 utilizing two types of transferrin",
  journal =      j-J-LAB-CLIN-MED,
  volume =       "63",
  number =       "3",
  pages =        "370--381",
  month =        mar,
  year =         "1967",
  CODEN =        "JLCMAK",
  ISSN =         "0022-2143 (print), 1532-6543 (electronic)",
  ISSN-L =       "0022-2143",
  bibdate =      "Tue Jun 21 18:26:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Lab. Clin. Med.",
  fjournal =     "Journal of Laboratory and Clinical Medicine",
}

@TechReport{Marsaglia:1968:OLRa,
  author =       "George Marsaglia and T. A. Bray",
  title =        "One-line random number generators and their use in
                 combinations",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "12",
  month =        mar,
  year =         "1968",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0667956",
  abstract =     "This is a discussion of some one-line random number
                 generators, requiring a single FORTRAN instruction,
                 together with a description of some short FORTRAN
                 programs which mix several such generators. Evidence
                 suggesting that the simple congruential generators are
                 unsatisfactory continues to grow; one of the most
                 promising alternatives is to mix several simple
                 generators. These composite generators do better in
                 various tests for randomness than do the simple
                 congruential generators used at many computer
                 centers.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1968:OLRb,
  author =       "George Marsaglia and T. A. Bray",
  title =        "One-line random number generators and their use in
                 combinations",
  journal =      j-CACM,
  volume =       "11",
  number =       "11",
  pages =        "757--759",
  month =        nov,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.15",
  MRnumber =     "39\#5040",
  MRreviewer =   "R. R. Coveyou",
  bibdate =      "Fri Nov 25 18:20:22 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 MathSciNet database",
  ZMnumber =     "0164.18802",
  abstract =     "Some one-line random number generators, i.e.
                 generators requiring a single FORTRAN instruction are
                 discussed, and some short FORTRAN programs which mix
                 several such generators are described. The aim is to
                 provide methods for incorporating random number
                 generators directly in FORTRAN programs, by means of a
                 few in-line instructions. The advantages are speed
                 (avoiding linkage to and from a subroutine),
                 convenience, and versatility. Anyone wishing to
                 experiment with generators, either using congruential
                 generators by themselves or mixing several generators
                 to provide a composite with potentially better
                 statistical properties than the library generators
                 currently available, may wish to consider some of the
                 simple FORTRAN program discussed here.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150E (General utility programs)",
  corpsource =   "Boeing Scientific Research Lab., Seattle, WA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "FORTRAN; Monte Carlo; numerical analysis; PRNG
                 (pseudo-random number generator); random number
                 generation; simulation; utility programs",
  ZMreviewer =   "R. R. Coveyou",
}

@Article{Marsaglia:1968:QPR,
  author =       "George Marsaglia",
  title =        "Query 27: Pseudo Random Normal Numbers",
  journal =      j-TECHNOMETRICS,
  volume =       "10",
  number =       "2",
  pages =        "401--402",
  month =        may,
  year =         "1968",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Mar 03 08:18:20 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstor.org/stable/1267057",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html;
                 http://www.tandfonline.com/loi/utch20",
}

@Article{Marsaglia:1968:RNF,
  author =       "George Marsaglia",
  title =        "Random numbers fall mainly in the planes",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "61",
  number =       "1",
  pages =        "25--28",
  day =          "15",
  month =        sep,
  year =         "1968",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.61.1.25",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  MRclass =      "65.15",
  MRnumber =     "38 \#3998",
  MRreviewer =   "R. R. Coveyou",
  bibdate =      "Thu Nov 14 11:39:48 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 MathSciNet database",
  note =         "A popularized account of this work appeared as ``Are
                 random numbers really random?'' [Scientific Research
                 (Philadelphia, PA), 3 (1968), 21--??]. This
                 widely-cited paper describes the hyperplane problem
                 that linear congruential generators suffer from,
                 although careful choice of multipliers can minimize its
                 importance: see
                 \cite{Coveyou:1967:FAU,Dyadkin:1997:SBM,Dyadkin:1997:FEL,Dyadkin:2000:SBM}.",
  ZMnumber =     "0172.21002",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
  keywords =     "numerical analysis; PRNG (pseudo-random number
                 generator)",
}

@TechReport{Marsaglia:1969:OSA,
  author =       "George Marsaglia",
  title =        "One-Sided Approximations by Linear Combinations of
                 Functions",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "18",
  month =        sep,
  year =         "1969",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0695796",
  abstract =     "The paper discusses how to approximate a function $
                 g(x) $ from one side by a linear combination of
                 functions $ f_1 (x), \ldots {}, f_n(x) $ so as to
                 minimize the area between the two. It discusses the
                 problem as one of finding the point where a moving
                 hyperplane last touches a convex set and an approximate
                 procedure based on linear programming methods. It gives
                 details of an algorithm for solving the problem,
                 examples, and applications to Monte Carlo Theory ---
                 generating random variables in a computer.",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:1969:RCR,
  author =       "George Marsaglia",
  title =        "Regularities in congruential random number
                 generators",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "8",
  month =        may,
  year =         "1969",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0689295",
  abstract =     "The paper suggests that points in $n$-space produced
                 by congruential random number generators are too
                 regular for general Monte Carlo use. Regularity was
                 established previously for multiplicative congruential
                 generators by showing that all the points fall in sets
                 of relatively few parallel hyperplanes. The existence
                 of many containing sets of parallel hyperplanes was
                 easily established, but proof that the number of
                 hyperplanes was small required a result of Minkowski
                 from the geometry of numbers --- a symmetric, convex
                 set of volume 2 to the nth power must contain at least
                 two points with integral coordinates. The present paper
                 takes a different approach to establishing the course
                 lattice structure of congruential generators. It gives
                 a simple, self-contained proof that points in $n$-space
                 produced by the general congruential generator $ r_(i +
                 1)$ is identically equal to $ a(r_i) + b \bmod m$ must
                 fall on a lattice with unit-cell volume at least $m$ to
                 the power $ (n - 1)$. There is no restriction on $a$ or
                 $b$; this means that all congruential random number
                 generators must be considered unsatisfactory in terms
                 of lattices containing the points they produce, for a
                 good generator of random integers should have an
                 $n$-lattice with unit-cell volume 1.",
  acknowledgement = ack-nhfb,
}

@Article{Cook:1970:FBM,
  author =       "J. D. Cook and G. Marsaglia and J. W. Eschbach and D.
                 D. Funk and C. A. Finch",
  title =        "Ferrokinetics: a biologic model for plasma iron
                 exchange in man",
  journal =      j-J-CLIN-INVEST,
  volume =       "49",
  number =       "2",
  pages =        "197--205",
  month =        feb,
  year =         "1970",
  CODEN =        "JCINAO",
  DOI =          "https://doi.org/10.1172/JCI106228",
  ISSN =         "0021-9738 (print), 1558-8238 (electronic)",
  ISSN-L =       "0021-9738",
  bibdate =      "Tue Jun 21 18:11:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC322461/;
                 http://www.pubmedcentral.gov/articlerender.fcgi?artid=322461",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Clin. Invest.",
  fjournal =     "Journal of Clinical Investigation",
  journal-URL =  "http://www.jci.org/archive",
}

@Article{Finch:1970:FM,
  author =       "C. A. Finch and K. Deubelbeiss and J. D. Cook and J.
                 W. Eschbach and L. A. Barker and D. D. Funk and G.
                 Marsaglia and R. S. Hillman and S. Slichter and J. W.
                 Adamson and A. Ganzoni and E. R. Giblett",
  title =        "Ferrokinetics in Man",
  journal =      j-MEDICINE,
  volume =       "49",
  number =       "1",
  pages =        "17--54",
  month =        jan,
  year =         "1970",
  CODEN =        "MEDIAV",
  ISSN =         "0025-7974 (print), 1536-5964 (electronic)",
  ISSN-L =       "0025-7974",
  bibdate =      "Tue Jun 21 18:03:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://journals.lww.com/md-journal/Citation/1970/01000/Ferrokinetics_in_Man.2.aspx",
  acknowledgement = ack-nhfb,
  fjournal =     "Medicine (Baltimore)",
}

@InCollection{Marsaglia:1970:OSA,
  author =       "G. Marsaglia",
  title =        "One-sided approximations by linear combinations of
                 functions",
  crossref =     "Talbot:1969:ATP",
  pages =        "233--242",
  year =         "1970",
  MRclass =      "65.30",
  MRnumber =     "42 \#1307",
  MRreviewer =   "G. Opfer",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0246.90027",
  ZMclass =      "*90-04 Machine computation, programs (optimization)
                 90C05 Linear programming 41A50 Best approximation",
}

@Article{Marsaglia:1970:RCR,
  author =       "George Marsaglia",
  title =        "Regularities in congruential random number
                 generators",
  journal =      j-NUM-MATH,
  volume =       "16",
  number =       "1",
  pages =        "8--10",
  year =         "1970",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.15",
  MRnumber =     "42 \#8651",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib;
                 MathSciNet database",
  ZMnumber =     "0212.18204",
  acknowledgement = ack-nhfb,
  classification = "C7890 (Other special applications of computing)",
  corpsource =   "Boeing Sci. Res. Labs., Seattle, WA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "random number generation",
  xxyear =       "1970/1971",
  ZMclass =      "*65C10 Random number generation",
}

@TechReport{Marsaglia:1970:RVI,
  author =       "George Marsaglia",
  title =        "Random Variables with Independent Binary Digits",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  pages =        "15",
  month =        jan,
  year =         "1970",
  bibdate =      "Wed Nov 12 07:42:28 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.dtic.mil/docs/citations/AD0705642",
  abstract =     "Let $ X = .b_1 b_2 b_3 \ldots {} $ be a random
                 variable with independent binary digits $ b_n $ taking
                 values $0$ or $1$ with probabilities $ p_n$ and $ q_n$.
                 When does $X$ have a density function? A continuous
                 density function? A singular distribution? This note
                 proves that the distribution $X$ is singular is and
                 only if the tail of the series $ \sum (\log (p_n /
                 q_n))$ squared diverges, and that $X$ has a density
                 that is positive on some interval if and only if $ \log
                 (p_n / q_n)$ is a geometric sequence with ratio $ 1 /
                 2$ for $n$ greater than some $k$, and in that case the
                 fractional part of $ 2^k X$ has an exponential density
                 (increasing or decreasing with the uniform density a
                 special case). It gives a sufficient condition for $X$
                 to have a density, ($ \sum \log (2 \max (p_n, q_n))$
                 converges), but unless the tail of the sequence $ \log
                 (p_n / q_n)$ is geometric, ratio $ 1 / 2$, the density
                 is a weird one that vanishes at least once in every
                 interval.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1971:MCC,
  author =       "George Marsaglia and E. D. Thomas",
  title =        "Mathematical Consideration of Cross Circulation and
                 Exchange",
  journal =      j-TRANSFUSION,
  volume =       "11",
  number =       "4",
  pages =        "216--219",
  month =        jul # "\slash " # aug,
  year =         "1971",
  CODEN =        "TRANAT",
  DOI =          "https://doi.org/10.1111/j.1537-2995.1971.tb04404.x",
  ISSN =         "0041-1132 (print), 1537-2995 (electronic)",
  ISSN-L =       "0041-1132",
  bibdate =      "Sat Jun 11 09:46:51 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "Equations are presented that describe the kinetics of
                 cross circulation and of exchange transfusion. These
                 equations should be useful in calculating the movement
                 of cells and metabolic substances between vascular and
                 extravascular compartments.",
  acknowledgement = ack-nhfb,
  fjournal =     "Transfusion (Bethesda)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1537-2995",
}

@Article{Marsaglia:1971:RVI,
  author =       "George Marsaglia",
  title =        "Random variables with independent binary digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "42",
  number =       "6",
  pages =        "1922--1929",
  month =        dec,
  year =         "1971",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177693058",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "60A05",
  MRnumber =     "45 \#7764",
  MRreviewer =   "A. Fuchs",
  bibdate =      "Fri Jan 6 09:58:57 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aoms/1177693058;
                 http://www.jstor.org/stable/2240118",
  ZMnumber =     "0239.60015",
  abstract =     "Let $ X = \cdot b_1 b_2 b_3 \cdots $ be a random
                 variable with independent binary digits $ b_n $ taking
                 values 0 or 1 with probability $ p_n $ and $ q_n = 1 -
                 p_n $. When does $X$ have a density? A continuous
                 density? A singular distribution? This note gives
                 necessary and sufficient conditions for the
                 distribution of $X$ to be: discrete: $ \Sigma \min
                 (p_n, q_n) < \infty $; singular: $ \Sigma^\infty_m
                 \lbrack \log (p_n / q_n) \rbrack^2 = \infty $ for every
                 $m$; absolutely continuous: $ \Sigma^\infty_m \lbrack
                 \log (p_n / q_n) \rbrack^2 < \infty $ for some $m$.
                 Furthermore, $X$ has a density that is bounded away
                 from zero on some interval if and only if $ \log (p_n /
                 q_n) $ is a geometric sequence with ratio $ \frac
                 {1}{2} $ for $ n > k $, and in that case the fractional
                 part of $ 2^k X $ has an exponential density
                 (increasing or decreasing with the uniform a special
                 case).",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  ZMclass =      "60E05 General theory of probability distributions
                 60F99 Limit theorems (probability)",
}

@Article{Marsaglia:1972:CPS,
  author =       "George Marsaglia",
  title =        "Choosing a point from the surface of a sphere",
  journal =      j-ANN-MATH-STAT,
  volume =       "43",
  number =       "2",
  pages =        "645--646",
  month =        apr,
  year =         "1972",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177692644",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65C10",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://projecteuclid.org/euclid.aoms/1177692644;
                 http://www.jstor.org/stable/2240001",
  ZMnumber =     "0248.65008",
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  ZMclass =      "*65C10 Random number generation",
}

@InCollection{Marsaglia:1972:SLC,
  author =       "George Marsaglia",
  title =        "The Structure of Linear Congruential Sequences",
  crossref =     "Zaremba:1972:ANT",
  pages =        "249--285",
  year =         "1972",
  MRclass =      "65C05",
  MRnumber =     "53 \#14854",
  MRreviewer =   "J. H. Halton",
  bibdate =      "Mon Aug 02 10:41:44 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0266.65007",
  acknowledgement = ack-nhfb,
  ZMclass =      "*65C10 Random number generation",
}

@Article{Marsaglia:1972:WD,
  author =       "G. Marsaglia and G. P. H. Styan",
  title =        "When does {$ {\rm rank} (A + B) = {\rm rank}(A) + {\rm
                 rank}(B) $}?",
  journal =      j-CAN-MATH-BULL,
  volume =       "15",
  number =       "3",
  pages =        "451--452",
  month =        "????",
  year =         "1972",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1972-082-8",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "15A03",
  MRnumber =     "47 \#236",
  MRreviewer =   "A. R. Amir-Moez",
  bibdate =      "Thu Sep 8 10:04:00 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v15/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0252.15002",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ZMclass =      "*15A03 Vector spaces",
}

@TechReport{Marsaglia:1973:HUM,
  author =       "George Marsaglia and K. Ananthanarayanan and A.
                 Zaman",
  title =        "How to use the {McGill} random-number package
                 {SUPER-DUPER}",
  type =         "Technical report",
  institution =  "School of Computer Science, McGill University",
  address =      "Montreal, Quebec, Canada",
  year =         "1973",
  bibdate =      "Thu Dec 20 20:19:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1974:APRa,
  author =       "George Marsaglia",
  title =        "Acknowledgement of priority to: {``Random variables
                 with independent binary digits'' (Ann. Math. Statist.
                 {\bf 42} (1971), 1922--1929)}",
  journal =      j-ANN-PROBAB,
  volume =       "2",
  number =       "4",
  pages =        "747--747",
  month =        aug,
  year =         "1974",
  CODEN =        "APBYAE",
  DOI =          "https://doi.org/10.1214/aop/1176996619",
  ISSN =         "0091-1798 (print), 2168-894X (electronic)",
  ISSN-L =       "0091-1798",
  MRclass =      "60A05",
  MRnumber =     "49 \#8070",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aop/1176996619",
  ZMnumber =     "0284.60018",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aop",
  ZMclass =      "60E05 General theory of probability distributions
                 60F99 Limit theorems (probability)",
}

@Article{Marsaglia:1974:APRb,
  author =       "George Marsaglia",
  title =        "Acknowledgement of priority to: {``Random variables
                 with independent binary digits'' (Ann. Math. Statist.
                 {\bf 42} (1971), 1922--1929)}",
  journal =      j-ANN-STAT,
  volume =       "2",
  number =       "4",
  pages =        "848--848",
  year =         "1974",
  CODEN =        "ASTSC7",
  DOI =          "https://doi.org/10.1214/aos/1176342776",
  ISSN =         "0090-5364 (print), 2168-8966 (electronic)",
  ISSN-L =       "0090-5364",
  MRclass =      "60A10",
  MRnumber =     "50 \#1310",
  MRreviewer =   "A. Fuchs",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aos/1176342776",
  ZMnumber =     "0284.60017",
  fjournal =     "Annals of Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aos/",
  ZMclass =      "*60E05 General theory of probability distributions
                 60F99 Limit theorems (probability)",
}

@Article{Marsaglia:1974:EIR,
  author =       "George Marsaglia and George P. H. Styan",
  title =        "Equalities and Inequalities for Ranks of Matrices",
  journal =      j-LIN-AND-MULT-ALGEBRA,
  volume =       "2",
  number =       "3",
  pages =        "269--292",
  year =         "1974",
  CODEN =        "LNMLAZ",
  DOI =          "https://doi.org/10.1080/03081087408817070",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  MRclass =      "15A45",
  MRnumber =     "52 \#5711",
  MRreviewer =   "A. R. Amir-Moez",
  bibdate =      "Tue Sep 20 15:09:41 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib;
                 MathSciNet database",
  ZMnumber =     "0297.15003",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
  onlinedate =   "03 Apr 2008",
  ZMclass =      "*15A03 Vector spaces 15A39 Linear inequalities 15A45
                 Miscellaneous inequalities involving matrices",
}

@Article{Marsaglia:1974:RCG,
  author =       "George Marsaglia and George P. H. Styan",
  title =        "Rank conditions for generalized inverses of
                 partitioned matrices",
  journal =      j-SANKHYA-A,
  volume =       "36",
  number =       "4",
  pages =        "437--442",
  month =        "10",
  year =         "1974",
  CODEN =        "SANABS",
  ISSN =         "0036-4452",
  ISSN-L =       "0036-4452",
  MRclass =      "15A09",
  MRnumber =     "52 \#5699",
  MRreviewer =   "Thomas L. Boullion",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0309.15002",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series A.
                 Methods and Techniques",
  journal-URL =  "https://www.jstor.org/journal/sankhyaseriesa",
  ZMclass =      "*15A09 Matrix inversion 15A03 Vector spaces",
}

@Article{Fillet:1975:IHI,
  author =       "G. Fillet and G. Marsaglia",
  title =        "Idiopathic Hemochromatosis ({IH}) --- Abnormality in
                 {RBC} Transport of Iron by Reticuloendothelial System
                 ({RES})",
  journal =      j-BLOOD,
  volume =       "46",
  number =       "6",
  pages =        "1007--1007",
  month =        "????",
  year =         "1975",
  CODEN =        "BLOOAW",
  ISSN =         "0006-4971 (print), 1528-0020 (electronic)",
  ISSN-L =       "0006-4971",
  bibdate =      "Mon Jun 3 19:13:11 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Blood",
}

@InCollection{Marsaglia:1975:EAL,
  author =       "G. Marsaglia",
  title =        "Extension and applications of {Lukacs}'
                 characterization of the gamma distribution",
  crossref =     "Saleh:1975:PSS",
  pages =        "13",
  year =         "1975",
  MRclass =      "62E10",
  MRnumber =     "55 \#6633",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  remark =       "Paper number 9.",
}

@Article{Marsaglia:1975:NLM,
  author =       "George Marsaglia and Alberto Tubilla",
  title =        "A Note on the ``Lack of Memory'' Property of the
                 Exponential Distribution",
  journal =      j-ANN-PROBAB,
  volume =       "3",
  number =       "2",
  pages =        "353--354",
  month =        apr,
  year =         "1975",
  CODEN =        "APBYAE",
  DOI =          "https://doi.org/10.1214/aop/1176996406",
  ISSN =         "0091-1798 (print), 2168-894X (electronic)",
  ISSN-L =       "0091-1798",
  MRclass =      "62E10",
  MRnumber =     "51 \#2073",
  MRreviewer =   "Ramesh C. Gupta",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aop/1176996406",
  ZMnumber =     "0336.60017",
  abstract =     "The exponential distribution is often characterized as
                 the only distribution with lack of memory. This note
                 points out a stronger result: the exponential is the
                 only distribution that is occasionally forgetful.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aop",
  ZMclass =      "*60E05 General theory of probability distributions
                 62E10 Structure theory of statistical distributions",
}

@Article{Marsaglia:1976:IFM,
  author =       "G. Marsaglia and K. Ananthanarayanan and N. J. Paul",
  title =        "Improvements on fast methods for generating normal
                 random variables",
  journal =      j-INFO-PROC-LETT,
  volume =       "5",
  number =       "2",
  pages =        "27--30",
  month =        jun,
  year =         "1976",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "65C10",
  MRnumber =     "55 \#11560",
  MRreviewer =   "I. Vaduva",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/ipl/ipl5.html#MarsagliaAP76;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib;
                 MathSciNet database",
  ZMnumber =     "0332.65003",
  acknowledgement = ack-nhfb,
  classification = "922; B0240G (Monte Carlo methods); C1140G (Monte
                 Carlo methods); C7890 (Other special applications of
                 computing)",
  corpsource =   "School of Computer Sci., McGill Univ., Montreal, Que.,
                 Canada",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "mathematical programming; mathematical statistics;
                 Monte Carlo; Monte Carlo methods; normal random
                 variables; random number generation; random numbers;
                 rectangle tooth tail method; simulation",
  oldlabel =     "MarsagliaAP76",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/ipl/MarsagliaAP76",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
}

@InCollection{Marsaglia:1976:RNG,
  author =       "George Marsaglia",
  title =        "Random number generation",
  crossref =     "Ralston:1976:ECS",
  pages =        "1192--1197",
  year =         "1976",
  bibdate =      "Mon Aug 02 16:34:17 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1977:SMG,
  author =       "George Marsaglia",
  title =        "The squeeze method for generating gamma variates",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "4",
  pages =        "321--325",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90089-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65C10",
  MRnumber =     "58 \#13613",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  ZMnumber =     "0384.65005",
  abstract =     "This paper describes an exact method for computer
                 generation of random variables with a gamma
                 distribution. The method is based on the
                 Wilson--Hilferty transformation and an improvement on
                 the rejection technique. The idea is to ``squeeze'' a
                 target density between two functions, the top one easy
                 to sample from, the bottom one easy to evaluate.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  ZMclass =      "*65C10 Random number generation 60E05 General theory
                 of probability distributions",
}

@Article{Skarberg:1978:PRK,
  author =       "Karl Skarberg and Mary Eng and Helmut Huebers and
                 George Marsaglia and Clement Finch",
  title =        "Plasma radioiron kinetics in man: explanation for the
                 effect of plasma iron concentration",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "75",
  number =       "3",
  pages =        "1559--1561",
  month =        mar,
  year =         "1978",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.75.3.1559",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Sat Jun 11 00:56:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.pnas.org/content/75/3/1559.short;
                 http://www.pubmedcentral.gov/articlerender.fcgi?artid=411513",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
}

@Article{Marsaglia:1980:CGN,
  author =       "George Marsaglia and I. J. Good",
  title =        "{C69}. {Generating} a normal sample with given sample
                 mean and variance",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "11",
  number =       "1",
  pages =        "71--74",
  year =         "1980",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949658008810390",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:47 MDT 2014",
  bibsource =    "http://jscs.stat.vt.edu/JSCS/articles/v11n1.html;
                 http://jscs.statjournals.net/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
                 http://www.tandf.co.uk/journals/titles/00949655.html;
                 Science Citation Index",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Marsaglia:1980:GRV,
  author =       "George Marsaglia",
  title =        "Generating random variables with a $t$-distribution",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "235--236",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2006231",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65C10",
  MRnumber =     "81a:65015",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1980.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database; MathSciNet database",
  ZMnumber =     "0423.65005",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; t-distribution",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
}

@InCollection{Marsaglia:1983:RNG,
  author =       "George Marsaglia",
  title =        "Random number generation",
  crossref =     "Ralston:1983:ECS",
  pages =        "1260--1264",
  year =         "1983",
  bibdate =      "Mon Aug 02 10:57:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Text virtually identical with first edition
                 \cite{Marsaglia:1976:RNG}. See also third edition
                 \cite{Marsaglia:1993:RNG}.",
}

@Article{Marsaglia:1983:RVI,
  author =       "George Marsaglia",
  title =        "Random variables with independent binary digits",
  journal =      "Kibern. Sb., Nov. Ser.",
  volume =       "20",
  pages =        "216--224",
  year =         "1983",
  CODEN =        "????",
  ISSN =         "0453-8382",
  bibdate =      "Fri Jan 6 09:50:41 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  ZMnumber =     "0535.60013",
  abstract =     "Translation from Ann. Math. Stat. 42, 1922--1929
                 (1971; Zbl 0239.60015).",
  acknowledgement = ack-nhfb,
  fjournal =     "Kiberneti{\v{c}}eskij sbornik. Novaya Seriya",
  fjournal-2 =   "Kiberneti{\c{c}}eskij sbornik (KS): sbornik statej",
  keywords =     "independent binary digits",
  language =     "Russian",
  ZMclass =      "*60E05 General theory of probability distributions
                 60F99 Limit theorems (probability)",
}

@Article{Marsaglia:1984:EAM,
  author =       "George Marsaglia",
  title =        "The exact-approximation method for generating random
                 variables in a computer",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "79",
  number =       "385",
  pages =        "218--221",
  month =        mar,
  year =         "1984",
  CODEN =        "JSTNAL",
  DOI =          "https://doi.org/10.2307/2288360",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "65C10",
  MRnumber =     "85d:65010",
  bibdate =      "Mon May 5 12:36:01 MDT 1997",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1984.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://www.jstor.org/stable/2288360",
  ZMnumber =     "0552.65005",
  abstract =     "A suitably chosen approximation to the inverse of a
                 probability distribution can lead to exact and very
                 fast methods for generating random variables, if the
                 approximation is made exact by adjusting the argument
                 of the approximating function. This article describes
                 the basic method and extensions of it. It gives four
                 examples, of which two are methods for generating
                 gamma-and t-variates that, while meant to illustrate
                 the basic method, show promise of being faster than the
                 best current methods.",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7634",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "gamma-and t-variates; inverse of a probability
                 distribution",
  location =     "SEL: Wi",
  revision =     "16/01/94",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
}

@Article{Marsaglia:1984:FEI,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "A fast, easily implemented method for sampling from
                 decreasing or symmetric unimodal density functions",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "5",
  number =       "2",
  pages =        "349--359",
  month =        jun,
  year =         "1984",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0905026",
  ISSN =         "0196-5204",
  MRclass =      "65U05 (65C10)",
  MRnumber =     "86a:65137",
  MRreviewer =   "Mervin Muller",
  bibdate =      "Tue Apr 29 19:18:28 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
                 MathSciNet database",
  ZMnumber =     "0573.65116",
  abstract =     "From authors' summary: The fastest computer methods
                 for sampling from a given density are those based on a
                 mixture of a fast and a slow part. This paper describes
                 a new method of this type, suitable for any decreasing
                 or symmetric unimodal density. It differs from others
                 in that it is faster and more easily implemented. It is
                 called the ziggurat method, after the shape of a
                 single, convenient density that provides for both the
                 fast and slow part of the generating process. Examples
                 are given for REXP and RNOR subroutines that generate
                 exponential and normal variates that, as assembler
                 routines, are nearly twice as fast as the previous
                 assembler routines, and that as Fortran routines,
                 approach the limiting possible speed appropriately
                 defined.",
  acknowledgement = ack-nhfb,
  annote =       "An updated version of this algorithm (see
                 \cite{Marsaglia:2000:ZMG}) is used in Matlab's randn()
                 function for generating normally-distributed
                 pseudo-random numbers; see \cite{Moler:2001:CCN}.",
  classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo
                 methods); C7310 (Mathematics computing)",
  corpsource =   "Computer Sci. Dept., Washington State Univ., Pullman,
                 WA, USA",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "exponential random variables; FORTRAN subroutine;
                 Fortran subroutines; Monte Carlo; Monte Carlo methods;
                 normal random variables; numerical analysis; random
                 numbers; REXP; RNOR; sampling; simulation; subroutines;
                 symmetric unimodal density functions; ziggurat method",
  treatment =    "N New Development; P Practical; T Theoretical or
                 Mathematical",
  ZMclass =      "*65C99 Numerical simulation 65C10 Random number
                 generation 62D05 Statistical sampling theory",
  ZMreviewer =   "L. Bondesson",
}

@Article{Marsaglia:1984:GCM,
  author =       "George Marsaglia and Ingram Olkin",
  title =        "Generating correlation matrices",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "5",
  number =       "2",
  pages =        "470--475",
  year =         "1984",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0905034",
  ISSN =         "0196-5204",
  MRclass =      "65C10 (62H99)",
  MRnumber =     "85h:65018",
  MRreviewer =   "G. P. Bhattacharjee",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib;
                 MathSciNet database",
  ZMnumber =     "0552.65006",
  abstract =     "This paper describes a variety of methods for
                 generating random correlation matrices, with emphasis
                 on choice of random variables and distributions so as
                 to provide matrices with given structure, expected
                 values of eigenvalues.",
  acknowledgement = ack-nhfb,
  classification = "B0240G (Monte Carlo methods); C1140G (Monte Carlo
                 methods)",
  corpsource =   "Computer Sci. Dept., Washington State Univ., Pullmann,
                 WA, USA",
  fjournal =     "Society for Industrial and Applied Mathematics.
                 Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "correlation matrices generation; eigenvalues;
                 eigenvalues and eigenfunctions; matrix algebra; Monte
                 Carlo methods; random correlation matrices; random
                 variables",
  treatment =    "T Theoretical or Mathematical",
  ZMclass =      "*65C10 Random number generation 65F30 Other matrix
                 algorithms 62J05 Linear regression",
}

@InProceedings{Marsaglia:1985:CVR,
  author =       "George Marsaglia",
  title =        "A Current View of Random Number Generators",
  crossref =     "Billard:1985:CSS",
  pages =        "3--10",
  year =         "1985",
  bibdate =      "Thu Dec 18 13:39:28 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://stat.fsu.edu/pub/diehard/;
                 http://www.evensen.org/marsaglia/keynote.ps",
  acknowledgement = ack-nhfb,
  remark =       "This paper introduces the Parking Lot test used in the
                 Diehard Battery test suite.",
}

@Article{Marsaglia:1985:MSR,
  author =       "George Marsaglia and Liang-Huei Tsay",
  title =        "Matrices and the structure of random number
                 sequences",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "67",
  pages =        "147--156",
  year =         "1985",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(85)90192-2",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65C10 (15A99)",
  MRnumber =     "86g:65018",
  MRreviewer =   "Gheorghe Barbu",
  bibdate =      "Thu Jan 23 11:18:08 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0572.65002",
  abstract =     "This paper discusses the maximum period and randomness
                 structure of two random number generators:
                 shift-register and lagged-Fibonacci. Two theorems on
                 the period of the random number generators are derived
                 using linear algebra and matrix theory. Some
                 regularities of m-tuples of points are shown for the
                 shift-register generators analogous to that for the
                 congruential random number generators. It is also
                 suggested that no such regularities are appeared for
                 the lagged-Fibonacci generators since lags are long
                 enough.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "lagged Fibonacci; maximal period; randomness;
                 shift-register",
  ZMclass =      "*65C10 Random number generation",
  ZMreviewer =   "K. Uosaki",
}

@Article{Marsaglia:1985:NPT,
  author =       "George Marsaglia",
  title =        "Note on a Proposed Test for Random Number Generators",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "756--758",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676623",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65C10",
  MRnumber =     "86h:65010",
  bibdate =      "Sun Jul 10 08:33:24 MDT 2011",
  bibsource =    "http://dblp.uni-trier.de/db/journals/tc/tc34.html#Marsaglia85;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib;
                 MathSciNet database",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676623",
  ZMnumber =     "0572.65001",
  abstract =     "This paper shows that many random number generators
                 with symmetric output would have the same mean as a
                 truly uniform random number generator in the recently
                 proposed test by {\it J. Savir} [IEEE Trans. Comput.
                 C-32, 960--961 (1983; Zbl 0518.65003)] and pass the
                 test. So, the author provides a better test based on
                 the exact distribution of the outcome of random number
                 sequences. The distribution is derived by using Markov
                 chain model.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Markov chain; test of randomness; uniform random
                 number",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/tc/Marsaglia85",
  ZMclass =      "*65C10 Random number generation",
  ZMreviewer =   "K. Uosaki",
}

@Article{Marsaglia:1986:IFC,
  author =       "George Marsaglia",
  title =        "The incomplete {$ \Gamma $} function as a continuous
                 {Poisson} distribution",
  journal =      j-COMPUT-MATH-APPL-B,
  volume =       "12",
  number =       "5--6",
  pages =        "1187--1190",
  month =        sep # "\slash " # dec,
  year =         "1986",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(86)90242-7",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0628.65149",
  abstract =     "The paper illustrates the use of the incomplete $
                 \Gamma $ function as a means for computer generation of
                 Poisson random variables.",
  abstract-2 =   "Among the many contributions of Professor Luke to the
                 theory of special functions, the most useful in
                 computational statistics is probably that on the
                 incomplete $\Gamma$ function. This short paper points
                 out that an incomplete $\Gamma$ function routine is so
                 important that it should be a standard part of any
                 library of statistical subroutines. The paper goes on
                 to give another example of use of the incomplete
                 $\Gamma$ function: as a means for computer generation
                 of Poisson random variables. and, having urged wide use
                 of the incomplete $\Gamma$ function, proceeds with
                 development of a Poisson generator whose principal aim
                 is to avoid use of the very function it has previously
                 lauded. Occasional use of an accurate incomplete
                 $\Gamma$ routine is essential however, in order that
                 the composite method be exact.",
  fjournal =     "Computers and Mathematics with Applications. Part B",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "computer generation of Poisson random variables;
                 incomplete gamma function",
  ZMclass =      "*65C99 Numerical simulation 65C10 Random number
                 generation 62E99 Statistical distribution theory 65D20
                 Computation of special functions",
  ZMreviewer =   "P. Reichensperger",
}

@Article{Tsang:1987:DTA,
  author =       "Wai Wan Tsang and George Marsaglia",
  title =        "A decision tree algorithm for squaring histograms in
                 random number generation",
  journal =      j-ARS-COMB,
  volume =       "23A",
  pages =        "291--301",
  year =         "1987",
  CODEN =        "????",
  ISSN =         "0381-7032",
  MRclass =      "65C10",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0614.65002",
  abstract =     "The squaring histogram method is a fast and flexible
                 way for generating random variables. It was developed
                 by the second author based upon the alias method
                 suggested by A. J. Walker. This paper describes a new
                 algorithm for the set-up procedure of the squaring
                 histogram method. The algorithm organizes data into a
                 binary search tree so that insertion of elements and
                 searching for minimum and maximum can be done in O(log
                 n) time. The average time complexity of the algorithm
                 is O(n log n) while the worst-case complexity is $
                 O(n^2) $. Empirical results confirm that the algorithm
                 runs much faster than the previously fastest algorithm
                 whose time complexity is $ O(n^2) $. Moreover, the
                 proposed algorithm can be implemented on a computer
                 without using more data storage than the existing
                 algorithms.",
  fjournal =     "Ars Combinatoria. The Canadian Journal of
                 Combinatorics",
  journal-URL =  "http://www.combinatorialmath.ca/arscombinatoria/",
  keywords =     "algorithms; average time complexity; random number
                 generation; squaring histogram method; worst-case
                 complexity",
  ZMclass =      "*65C10 Random number generation",
}

@Article{Marsaglia:1989:CAA,
  author =       "George Marsaglia and Arif Zaman and Youlu Zheng",
  title =        "{C309}: An Algorithm for the Area of the Union of a
                 Collection of Convex Sets",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "31",
  number =       "1",
  pages =        "46--49",
  month =        "????",
  year =         "1989",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949658908811112",
  ISSN =         "0094-9655 (print), 1563-5163 (electronic)",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Aug 05 09:22:20 2004",
  bibsource =    "http://jscs.stat.vt.edu/JSCS/articles/v31n1.html;
                 http://jscs.statjournals.net/;
                 http://web.lums.edu.pk/~arifz/resume.html;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 http://www.tandf.co.uk/journals/titles/00949655.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@InCollection{Marsaglia:1989:CGD,
  author =       "George Marsaglia",
  title =        "The {$ X + Y, \; X / Y $} characterization of the
                 gamma distribution",
  crossref =     "Gleser:1989:CPS",
  pages =        "91--98",
  year =         "1989",
  MRclass =      "60E10 (62E10)",
  MRnumber =     "91a:60049",
  MRreviewer =   "Moshe Shaked",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
}

@Article{Marsaglia:1989:NSS,
  author =       "George Marsaglia and Arif Zaman and John C. W.
                 Marsaglia",
  title =        "Numerical solution of some classical
                 differential-difference equations",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "191--201",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008355",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L05 (65Q05)",
  MRnumber =     "90h:65124",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database; MathSciNet database",
  ZMnumber =     "0675.65073",
  abstract =     "This article describes a method for evaluating of
                 Renyi's, Dickman's and Buchstab's functions with
                 defining relations, respectively: $ [(x - 1)f(x)]' = 2
                 f(x - 1), $ $ X V'(x) = - V(x - 1) $ and $ [X W(x)]' =
                 W(x - 1), $ respectively. The method gives numerical
                 solutions accurate to hundreds or even thousands of
                 digits.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4170 (Differential equations); C1120 (Analysis)",
  corpsource =   "Dept. of Stat., Florida State Univ., Tallahassee, FL,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Buchstab's function; classical differential-difference
                 equations; classical problems; Dickman's function;
                 difference equations; differential equations;
                 differential-difference equations; numerical; Renyi's
                 function; solutions",
  treatment =    "T Theoretical or Mathematical",
  ZMclass =      "*65L05 Initial value problems for ODE (numerical
                 methods) 65D20 Computation of special functions 34K05
                 General theory of functional-differential equations",
  ZMreviewer =   "P. I. Ialamov",
}

@InProceedings{Marsaglia:1989:RVS,
  author =       "George Marsaglia",
  title =        "Random Variables for Supercomputers",
  crossref =     "Wegman:1988:SIC",
  pages =        "103--103",
  year =         "1989",
  bibdate =      "Wed Nov 12 16:33:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Abstract only.",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a205068.pdf",
  abstract =     "A discussion of methods for generating random
                 variables in supercomputers, particularly the 205 and
                 ETA 10. Methods that exploit vector processing are
                 well-suited for generating uniform random variables,
                 both integer and real, and several of them are
                 described. For non-uniform variates, however, methods
                 that have proved best for conventional computers do not
                 readily yield to vector methods. For example, the best
                 methods for normal or exponential variates in
                 conventional computers take less than $ 1.2 T $, where
                 $T$ is the time for a uniform variate, yet in
                 supercomputers those methods take relatively much
                 longer. Different approaches to reducing these times
                 will be discussed.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1990:DBR,
  author =       "George Marsaglia and B. Narasimhan and Arif Zaman",
  title =        "The distance between random points in rectangles",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "19",
  number =       "11",
  pages =        "4199--4212",
  year =         "1990",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610929008830437",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  MRclass =      "60D05 (62E15)",
  MRnumber =     "92b:60015",
  bibdate =      "Wed Jan 27 05:38:53 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  ZMnumber =     "0731.60012",
  abstract =     "Consider two oriented rectangles in $ {\bbfR }^2 $
                 with sides parallel to the x and y axes, possibly
                 overlapping or even coincident; choose a point randomly
                 and uniformly in each rectangle. This paper describes a
                 method for finding the distribution function for the
                 random distance between the points. The required
                 density is described as a sum of elementary integrals
                 whose computation is then reduced to evaluations of one
                 particular function. For this a Fortran program is
                 described. Several special cases are treated more
                 specifically.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
  keywords =     "Fortran program; random distance between the points",
  ZMclass =      "60D05 Geometric probability 60-04 Machine computation,
                 programs (probability theory)",
  ZMreviewer =   "W. J. Firey (Corvallis)",
}

@Article{Marsaglia:1990:NDS,
  author =       "George Marsaglia and John C. W. Marsaglia",
  title =        "A new derivation of {Stirling}'s approximation to $ n!
                 $",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "97",
  number =       "9",
  pages =        "826--829",
  month =        nov,
  year =         "1990",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324749",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "41A60 (01A50 05A10)",
  MRnumber =     "92b:41049",
  MRreviewer =   "E. Rodney Canfield",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 MathSciNet database",
  ZMnumber =     "0786.05007",
  abstract =     "A derivation of Stirling's formula $ n! \sim n^n
                 e^{-n} \sqrt {2 \pi n^n} $ is presented. To this
                 purpose the authors consider the relation $ n! =
                 \int^\infty_0 x^n e^{-x} \, d x $. Their proof is not
                 new; see {\it Nathaniel Grossman} [Letter to the
                 editor, Am. Math. Mon. 98, No. 3, 233 (1991)].",
  fjournal =     "The American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "approximation to limiting values; binomial
                 coefficients; factorials; Stirling's formula",
  ZMclass =      "*05A10 Combinatorial functions 40A25 Approximation to
                 limiting values 26A09 Elementary functions of one real
                 variable 41A60 Asymptotic problems in approximation",
  ZMreviewer =   "D. Acu (Sibiu)",
}

@Article{Marsaglia:1990:RNG,
  author =       "George Marsaglia and B. Narasimhan and Arif Zaman",
  title =        "A random number generator for {PC}'s",
  journal =      j-COMP-PHYS-COMM,
  volume =       "60",
  number =       "3",
  pages =        "345--349",
  month =        oct,
  year =         "1990",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(90)90033-W",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65C10",
  MRnumber =     "1 076 268",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 MathSciNet database",
  ZMnumber =     "0997.65510",
  abstract =     "It is now possible to do serious scientific work on
                 personal computers (PC's). Many simulation studies,
                 whether exploratory or for production runs, call for
                 random numbers. We offer here a new kind of random
                 number generator with implementation tailored
                 specifically for PC's using Intel 8088/8086 or
                 80286/80386 processors. A floating-point coprocessor is
                 not required or even useful for the generator,
                 although, of course, a coprocessor may help other parts
                 of a simulation. The generator has an extremely long
                 period --- some 2^{1407} --- requires only 43 stored
                 values and uses only one arithmetic operation:
                 subtraction. It is one of a new class of generators
                 that we have recently developed. They are called
                 add-with-carry and subtract-with-borrow generators.
                 Related to lagged-Fibonacci generators, the new class
                 has an interesting underlying theory, astonishingly
                 long periods and provable uniformity for full
                 sequences. This article describes a machine language
                 subroutine that provides 32-bit random integers as well
                 as uniform (single precision) reals with standard
                 24-bit fractions.",
  fjournal =     "Computer Physics Communications. An International
                 Journal and Program Library for Computational Physics
                 and Physical Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  ZMclass =      "*65C10 Random number generation",
}

@Article{Marsaglia:1990:TUR,
  author =       "George Marsaglia and Arif Zaman and Wai Wan Tsang",
  title =        "Toward a universal random number generator",
  journal =      j-STAT-PROB-LETT,
  volume =       "9",
  number =       "1",
  pages =        "35--39",
  month =        jan,
  year =         "1990",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(90)90092-L",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65C10",
  MRnumber =     "91a:65008",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/1990.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0692.65001",
  abstract-1 =   "This paper presents a ``universal'' random number
                 generator that is able to produce the same sequence of
                 random variables in a wide variety of computers and
                 that passes some tests of randomness and independence.
                 The generator combines two different generators: a
                 lagged-Fibonacci generator $F(97,33.\cdot)$ and a
                 simple arithmetic sequence for the prime modulus
                 $2^{24}-3$. Results of a randomness test are presented
                 and a Fortran implementation of the generator is
                 suggested.",
  abstract-2 =   "This article describes an approach towards a random
                 number generator that passes all of the stringent tests
                 for randomness we have put to it, and that is able to
                 produce exactly the same sequence of uniform random
                 variables in a wide variety of computers, including
                 TRS80, Apple, Mackintosh, Commodore, Kaypro, IBM PC,
                 AT, PC and AT clones, Sun, Vax, IBM 360/370, 3090,
                 Amdahl, CDC Cyber and even 205 ETA supercomputers.",
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "arithmetic sequence; Fortran implementation;
                 independence test; lagged-Fibonacci generator;
                 randomness test; universal random number generator",
  ZMclass =      "*65C10 Random number generation",
  ZMreviewer =   "K. Uosaki",
}

@Article{Zaman:1990:RSS,
  author =       "Arif Zaman and George Marsaglia",
  title =        "Random Selection of Subsets with Specified Element
                 Probabilities",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "19",
  number =       "11",
  pages =        "4419--4434",
  month =        "????",
  year =         "1990",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610929008830448",
  ISSN =         "0361-0926 (print), 1532-415x (electronic)",
  ISSN-L =       "0361-0926",
  bibdate =      "Thu Aug 05 06:44:44 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  abstract =     "A lottery ticket consists of a choice of 6 numbers,
                 all different, from 1 to 49. Most probability analysis
                 assumes that this is like sampling without replacement
                 from an urn. On the other hand, it is well known that
                 many people pick 'lucky' numbers such as 7 and 11 more
                 frequently than 'ordinary' numbers such as 17 or 26.
                 For some lotteries, information is available on the
                 frequencies with which players have chosen each of the
                 numbers from 1 to 49. This raises the interesting
                 question of finding distributions on the $ 49 \choose 6
                 $ possible ticket choices that will be consistent with
                 the frequencies specified for each of the elements. We
                 develop several methods for doing this; some of them
                 may be extended to the next stages of the problem, when
                 enough information is available from the Lottery to
                 specify frequencies of pairs or even triples, and one
                 seeks distributions on the 6-tuples consistent with
                 those frequencies.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics. Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}

@Article{Marsaglia:1991:NCR,
  author =       "George Marsaglia and Arif Zaman",
  title =        "A new class of random number generators",
  journal =      j-ANN-APPL-PROBAB,
  volume =       "1",
  number =       "3",
  pages =        "462--480",
  month =        aug,
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1214/aoap/1177005878",
  ISSN =         "1050-5164",
  MRclass =      "65C10",
  MRnumber =     "92h:65009",
  MRreviewer =   "Renata Rotondi",
  bibdate =      "Mon Aug 02 11:01:47 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  URL =          "http://projecteuclid.org/euclid.aoap/1177005878",
  ZMnumber =     "0733.65005",
  abstract =     "We introduce a new class of generators of two types:
                 add-with-carry and subtract-with-borrow. Related to
                 lagged-Fibonacci generators, the new class has
                 interesting underlying theory, astonishingly long
                 periods and provable uniformity for full sequences.
                 Among several that we mention, we recommend
                 particularly promising ones that will generate a
                 sequence of 2e1751 bits.",
  abstract-2 =   "We introduce a new class of generators of two types:
                 add-with-carry and subtract-with-borrow. Related to
                 lagged-Fibonacci generators, the new class has
                 interesting underlying theory, astonishingly long
                 periods and provable uniformity for full sequences.
                 Among several that we mention, we recommend
                 particularly promising ones that will generate a
                 sequence of $2^{1751}$ bits, or a sequence of
                 $2^{1376}$ 32-bit integers, or a sequence of $2^{931}$
                 reals with 24-bit fractions--all using simple computer
                 arithmetic (subtraction) and a few memory locations.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Annals of Applied Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoap/;
                 http://www.jstor.org/journals/10505164.html",
  keywords =     "add with carry generator; lagged Fibonacci generator;
                 Monte Carlo methods; numerical examples; random number
                 generators; subtract-with-borrow generators; very long
                 period sequences",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
  ZMreviewer =   "M. Cugiani (Milano)",
}

@Article{Marsaglia:1991:NGR,
  author =       "George Marsaglia",
  title =        "Normal ({Gaussian}) Random Variables for
                 Supercomputers",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "5",
  number =       "1",
  pages =        "49--55",
  month =        jun,
  year =         "1991",
  CODEN =        "JOSUED",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Mon Jun 2 19:03:29 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Stat., Florida State Univ., Tallahassee, FL,
                 USA",
  classification = "C1140G (Monte Carlo methods); C1140Z (Other and
                 miscellaneous); C5440 (Multiprocessor systems and
                 techniques); C7310 (Mathematics)",
  corpsource =   "Dept. of Stat., Florida State Univ., Tallahassee, FL,
                 USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "efficient constant-time methods; exponential random
                 variables; Gaussian random variables; Monte Carlo
                 methods; Monte Carlo studies; normal distribution
                 function; parallel machines; parallel operations;
                 probability; statistical analysis; supercomputers",
  treatment =    "P Practical",
}

@InCollection{Marsaglia:1992:MRN,
  author =       "George Marsaglia",
  title =        "The mathematics of random number generators",
  crossref =     "Burr:1992:UEN",
  pages =        "73--90",
  year =         "1992",
  MRclass =      "11K45 (65C10)",
  MRnumber =     "94a:11119",
  MRreviewer =   "R. G. Stoneham",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  series =       "Proc. Sympos. Appl. Math.",
  ZMnumber =     "0776.65005",
  abstract =     "[For the entire collection see Zbl 0759.00006.]\par
                 This paper first describes the role of number theory
                 for the three most common classes of random number
                 generators such as congruential, shift- register, and
                 lagged-Fibonacci generators. A condition characterizing
                 full-period sequences for shift-register generators is
                 given its proof sketched, which also plays a role
                 establishing the periods of lagged- Fibonacci
                 generators. Then, more details are given for the
                 mathematics of a new class of random number generators
                 with quite long periods, called `add-with-carry' and
                 `subtract-with-borrow' generators [the author and {\it
                 A. Zaman}, Ann. Appl. Probab., 1, No. 3, 462--480
                 (1991; Zbl 0733.65005)]. A table listing examples of
                 some of the most common random number generators
                 including the classes mentioned above is given at the
                 end of this paper.",
  keywords =     "add-with-carry generator; congruential generators;
                 lagged-Fibonacci generators; number theory; random
                 number generators; shift-register generators;
                 subtract-with-borrow generator",
  ZMclass =      "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc. 11A07 Congruences, etc. 11A63 Radix
                 representation",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@TechReport{Marsaglia:1993:KG,
  author =       "George Marsaglia and Arif Zaman",
  title =        "The {KISS} generator",
  type =         "Technical report",
  number =       "??",
  institution =  "Department of Statistics, Florida State University",
  address =      "Tallahassee, FL, USA",
  month =        "????",
  year =         "1993",
  bibdate =      "Sat Mar 08 15:05:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "See report of cryptographic insecurity of KISS
                 generator \cite{Rose:2011:KBT}. See also
                 \cite{Robert:1999:MCS}.",
  acknowledgement = ack-nhfb,
  remark =       "Check address: some citations show University of
                 Florida, Gainesville, but the lead author worked at
                 FSU. I cannot find this report in either the FSU or UF
                 libraries, or their Departments of Statistics.",
}

@Article{Marsaglia:1993:LHR,
  author =       "George Marsaglia and Arif Zaman",
  title =        "Letter: How Random Is Random Enough?",
  journal =      j-SCIENCE-NEWS,
  volume =       "143",
  number =       "11",
  pages =        "163--163",
  day =          "13",
  month =        mar,
  year =         "1993",
  CODEN =        "SCNEBK",
  ISSN =         "0036-8423 (print), 1943-0930 (electronic)",
  ISSN-L =       "0036-8423",
  bibdate =      "Wed Jun 22 06:40:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Cautionary comment on \cite{Peterson:1992:MCP}.",
  URL =          "http://www.jstor.org/stable/10.2307/3977245",
  acknowledgement = ack-nhfb,
  ajournal =     "Sci. News (Washington, DC)",
  fjournal =     "Science News (Washington, DC)",
  journal-URL =  "http://www.jstor.org/journals/00368423.html;
                 http://www.sciencenews.org/view/archives;
                 http://www3.interscience.wiley.com/journal/122396840/home",
}

@Article{Marsaglia:1993:MTR,
  author =       "George Marsaglia and Arif Zaman",
  title =        "Monkey Tests for Random Number Generators",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "26",
  number =       "9",
  pages =        "1--10",
  month =        nov,
  year =         "1993",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(93)90001-C",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65C10",
  MRnumber =     "1 236 767",
  bibdate =      "Mon Aug 02 10:36:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib;
                 MathSciNet database",
  note =         "See also \cite{Percus:1995:TAM}.",
  ZMnumber =     "0788.65007",
  abstract =     "This paper describes some simple but sophisticated
                 tests of suitability of certain random number
                 generators (RNG's). The generators are used to provide
                 the random keystrokes. The overlapping $m$-tuples of
                 successive elements in random sequences are used for
                 assessing both uniformity and independence in the
                 output of a random number generator.\par One is CAT
                 test: RNG has a typewriter with 26 upper-case letters
                 and how many keystrokes needed to spell CAT is tested.
                 The others are OPSO
                 (Overlapping-Pairs-Sparse-Occupancy), OTSO
                 (Overlapping-Triples-Sparse- Occupancy), OQSO
                 (Overlapping-Quadruples-Sparse-Occupancy) and DNA
                 tests: how many missing $k$-letter words in a long
                 string of $n$ random keystrokes from an alphabet of $
                 \alpha $ letters are tested.\par Examples of RNG's in
                 classes of congruential generators, shift register
                 generators, lagged Fibonacci generators, add-with-carry
                 and subtract-and- carry generators and combination
                 generators, passing these tests are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "congruential generators; lagged Fibonacci generators;
                 monkey tests; Overlapping-Pairs-Sparse-Occupancy;
                 Overlapping-Quadruples-Sparse-Occupancy;
                 Overlapping-Triples-Sparse-Occupancy; random number
                 generators; shift register generators; sparse-occupancy
                 tests",
  ZMclass =      "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@InCollection{Marsaglia:1993:RNG,
  author =       "George Marsaglia",
  title =        "Random Number Generation",
  crossref =     "Ralston:1993:ECS",
  pages =        "1145--1148",
  year =         "1993",
  bibdate =      "Mon Aug 02 16:28:18 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Text substantially rewritten from second edition
                 \cite{Marsaglia:1983:RNG}.",
}

@Article{Marsaglia:1993:SIS,
  author =       "G. Marsaglia and B. Narasimhan",
  title =        "Simulating interpolation search",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "26",
  number =       "8",
  pages =        "31--42",
  month =        oct,
  year =         "1993",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(93)90329-T",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "68P10",
  MRnumber =     "94h:68041",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  ZMnumber =     "0800.68353",
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "efficient algorithm; interpolation search; searching
                 ordered tables",
  ZMclass =      "*68P10 Searching and sorting 65C99 Numerical
                 simulation",
}

@Article{Marsaglia:1993:TCR,
  author =       "George Marsaglia",
  title =        "Technical Correspondence: Remarks on Choosing and
                 Implementing Random Number Generators",
  journal =      j-CACM,
  volume =       "36",
  number =       "7",
  pages =        "105--108",
  month =        jul,
  year =         "1993",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/159544.376068",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jan 28 14:57:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  remark =       "Marsaglia criticizes the `minimal-standard generator'
                 proposed in \cite{Park:1988:RNG} and discusses fast
                 ways to compute LCGs with particular multipliers. See
                 new test in \cite{Sullivan:1993:ATR} and responses in
                 \cite{Park:1993:ATR}.",
}

@Misc{Marsaglia:1994:MAR,
  author =       "George Marsaglia",
  title =        "The mother of all random generators",
  howpublished = "Web document",
  month =        oct,
  year =         "1994",
  bibdate =      "Tue Jun 21 18:41:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "ftp://ftp.taygeta.com/pub/c/mother.c",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1994:REI,
  author =       "George Marsaglia and Arif Zaman and John C. W.
                 Marsaglia",
  title =        "Rapid evaluation of the inverse of the normal
                 distribution function",
  journal =      j-STAT-PROB-LETT,
  volume =       "19",
  number =       "4",
  pages =        "259--266",
  day =          "15",
  month =        mar,
  year =         "1994",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(94)90174-0",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65U05",
  MRnumber =     "1 278 658",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett1990.bib;
                 MathSciNet database",
  URL =          "http://www.sciencedirect.com/science/article/pii/0167715294901740",
  ZMnumber =     "0798.65132",
  abstract =     "This is an interesting article with direct application
                 in generating normal random variable by computer
                 programs. The suggested applications are related to
                 Monte Carlo simulation based on massively parallel
                 systems or supercomputers. The idea is to replace
                 larger programs with complicated computations and with
                 difficulties in accuracy controlling by simpler
                 arithmetic programs that use tabled constants. These
                 seem to be the normal evolution since memory becomes
                 cheaper and cheaper.\par

                 The authors compute the inverse of the cPhi function $$
                 c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
                 t^2 / 2) d t = u, $$ using a uniform random variable as
                 input and the truncated Taylor series development of
                 it. In order to increase the speed the coefficients of
                 the truncated Taylor series $$ x(u_0 + h) = x(u_0) +
                 x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1
                 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for
                 1024 points. And here comes another bright idea: the
                 1024 points are chosen based on the representation of
                 the uniform random variable in modern computers as
                 floating point variable of the form: $ u = 2^{-k} ((1 /
                 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0
                 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
                 & l t; 2^{18} $ and considering 32 bit
                 representation.\par

                 With this assumptions and the truncation to the third
                 power of $h$ of the Taylor series, the authors show
                 that the error does not exceed the limit of single
                 precision accuracy. Furthermore the calculations are
                 speeded up based on reducing multiplications. A number
                 of FORTRAN programs are also presented in order to
                 evaluate the complementary normal distribution function
                 cPhi (several versions) with great accuracy, create the
                 constant tables, and generate the normal distribution
                 variable. These simple programs give the user the
                 possibility to completely control the accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "cPhi function; FORTRAN programs; massive parallel
                 systems; Monte Carlo simulation; normal distribution
                 function; normal random variable; supercomputers;
                 truncated Taylor series",
  ZMclass =      "*65C99 Numerical simulation 65C05 Monte Carlo methods
                 60-04 Machine computation, programs (probability
                 theory) 60E05 General theory of probability
                 distributions 62E17 Approximations to statistical
                 distributions (nonasymptotic)",
  ZMreviewer =   "A. Pasculescu (Bucuresti)",
}

@Article{Marsaglia:1994:SPV,
  author =       "George Marsaglia and Arif Zaman",
  title =        "Some portable very-long-period random number
                 generators",
  journal =      j-COMPUT-PHYS,
  volume =       "8",
  number =       "1",
  pages =        "117--121",
  month =        jan # "\slash " # feb,
  year =         "1994",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168514",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Mon Aug 02 17:54:20 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168514",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
  remark =       "ran2() range is [1,2147483562], with period about
                 2.3e+18. mzran13() has range[0,2147483647] and period
                 about 2^125 = 4.25e37.",
}

@Misc{Marsaglia:1994:YAR,
  author =       "George Marsaglia",
  title =        "Yet another rug",
  howpublished = "Posted to the electronic billboard {\tt
                 sci.stat.math}.",
  day =          "1",
  month =        aug,
  year =         "1994",
  bibdate =      "Thu Jan 05 15:49:10 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Marsaglia:1995:MRN,
  author =       "George Marsaglia",
  title =        "The {Marsaglia} Random Number {CDROM} including the
                 {Diehard Battery of Tests} of Randomness",
  howpublished = "Web site at the Department of Statistics, Florida
                 State University, Tallahassee, FL, USA.",
  year =         "1995",
  bibdate =      "Sat Mar 03 07:40:23 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://stat.fsu.edu/pub/diehard/",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1995:RVI,
  author =       "G. Marsaglia",
  title =        "Random variables with independent integer and
                 fractional parts",
  journal =      j-STAT-NEERLANDICA,
  volume =       "49",
  number =       "2",
  pages =        "133--137",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1467-9574.1995.tb01460.x",
  ISSN =         "0039-0402 (print), 1467-9574 (electronic)",
  ISSN-L =       "0039-0402",
  MRclass =      "62E10",
  MRnumber =     "96d:62013",
  bibdate =      "Tue Oct 8 09:13:07 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/stat-neerlandica.bib;
                 MathSciNet database",
  ZMnumber =     "0831.62015",
  abstract =     "For random variables with independent integer and
                 fractional parts a canonical form is given for those
                 with positive differentiable densities, and a condition
                 ensuring exponentiality is made less restrictive.",
  acknowledgement = ack-nhfb,
  ajournal =     "Stat. Neerl.",
  fjournal =     "Statistica Neerlandica. Journal of the Netherlands
                 Society for Statistics and Operations Research",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9574",
  keywords =     "canonical form; characterizations; exponential
                 distribution; independent digits; independent integer
                 and fractional parts; positive differentiable
                 densities",
  onlinedate =   "29 April 2008",
  ZMclass =      "*62E10 Structure theory of statistical distributions
                 60E05 General theory of probability distributions",
}

@TechReport{Marsaglia:1996:DBT,
  author =       "George Marsaglia",
  title =        "{DIEHARD}: {A} Battery of Tests of Randomness",
  type =         "Technical report",
  number =       "??",
  institution =  "Florida State University",
  address =      "Tallahassee, FL, USA",
  year =         "1996",
  bibdate =      "Mon Aug 02 10:51:00 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://euler.bd.psu.edu/~naras/diehard/snapshots.html;
                 http://stat.fsu.edu/~geo/",
  acknowledgement = ack-nhfb,
}

@Misc{Marsaglia:1997:RNG,
  author =       "George Marsaglia",
  title =        "A random number generator for {C}",
  howpublished = "Posted to the {\tt sci.math.num-analysis} news group",
  day =          "29",
  month =        sep,
  year =         "1997",
  bibdate =      "Thu Dec 20 20:21:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "From the posting: ``Keep the following six lines of
                 code somewhere in your files.

                 \#define znew ((z=36969*(z\&65535)+(z>>16))<<16)
                 \#define wnew ((w=18000*(w\&65535)+(w>>16))\&65535)
                 \#define IUNI (znew+wnew) \#define UNI
                 (znew+wnew)*4.656613e-10 static unsigned long
                 z=362436069, w=521288629; void setseed(unsigned long
                 i1,unsigned long i2){z=i1; w=i2;}

                 Whenever you need random integers or random reals in
                 your C program, just insert those six lines at (near?)
                 the beginning of the program. In every expression where
                 you want a random real in [0,1) use UNI, or use IUNI
                 for a random 32-bit integer. No need to mess with
                 ranf() or ranf(lastI), etc, with their requisite
                 overheads. Choices for replacing the two multipliers
                 36969 and 18000 are given below. Thus you can tailor
                 your own in-line multiply-with-carry random number
                 generator.''",
  URL =          "http://mathforum.org/kb/thread.jspa?messageID=1607565",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1998:MPMa,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "The {Monty Python} Method for Generating Gamma
                 Variables",
  journal =      j-J-STAT-SOFT,
  volume =       "3",
  number =       "3",
  pages =        "1--8",
  year =         "1998",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sun Nov 17 22:35:43 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib",
  URL =          "http://www.jstatsoft.org/v03/i03;
                 http://www.jstatsoft.org/v03/i03/GERMGAM.PDF;
                 http://www.jstatsoft.org/v03/i03/GERMGAM.PS;
                 http://www.jstatsoft.org/v03/i03/updates",
  abstract =     "The Monty Python Method for generating random
                 variables takes a decreasing density, cuts it into
                 three pieces, then, using area-preserving
                 transformations, folds it into a rectangle of area $1$.
                 A random point $ (x, y) $ from that rectangle is used
                 to provide a variate from the given density, most of
                 the time as $x$ itself or a linear function of $x$. The
                 decreasing density is usually the right half of a
                 symmetric density.\par

                 The Monty Python method has provided short and fast
                 generators for normal, $t$ and von Mises densities,
                 requiring, on the average, from $ 1.5 $ to $ 1.8 $
                 uniform variables. In this article, we apply the method
                 to non-symmetric densities, particularly the important
                 gamma densities. We lose some of the speed and
                 simplicity of the symmetric densities, but still get a
                 method for variates that is simple and fast enough to
                 provide beta variates in the form $ \gamma_a =
                 (\gamma_a + \gamma_b) $. We use an average of less than
                 $ 1.7 $ uniform variates to produce a gamma variate
                 whenever $ \alpha \geq 1 $. Implementation is simpler
                 and from three to five times as fast as a recent method
                 reputed to be the best for changing $ \alpha $ s.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@Article{Marsaglia:1998:MPMb,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "The {Monty Python} method for generating random
                 variables",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "341--350",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292453",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (60E99)",
  MRnumber =     "99k:65014",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 MathSciNet database",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/",
  ZMnumber =     "0930.65002",
  abstract =     "We suggest an interesting and fast method for
                 generating normal, exponential, $t$, von Mises, and
                 certain other important random variables used in Monte
                 Carlo studies. The right half of a symmetric density is
                 cut into pieces, then, using simple area-preserving
                 transformations, reassembled into a rectangle from
                 which the $x$-coordinate---or a linear function of the
                 $x$-coordinate---of a random point provides the
                 required variate. To illustrate the speed and
                 simplicity of the Monty Python method, we provide a
                 small C program, self-contained, for rapid generation
                 of normal (Gaussian) variables. It is self-contained in
                 the sense that required uniform variates are generated
                 in-line, as pairs of 16-bit integers by means of the
                 remarkable new multiply-with-carry method.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
  journal-URL =  "http://portal.acm.org/toc.cfm?idx=J782",
  keywords =     "$t$ variates; algorithms; Monte Carlo studies; Monty
                 Python method; normal variates; random variable
                 generation; theory; von Mises variates",
  subject =      "{\bf G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf I.6.1} Computing Methodologies,
                 SIMULATION AND MODELING, Simulation Theory.",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
}

@Misc{Marsaglia:1999:RNC,
  author =       "George Marsaglia",
  title =        "Random numbers for {C}: The {END}?",
  howpublished = "Message-ID {\tt 36A5FC62.17C9CC33@stat.fsu.edu}.
                 Posting to the {\tt sci.crypt.random-numbers}, {\tt
                 sci.math}, and {\tt sci.stat.math} news groups.",
  day =          "20",
  month =        jan,
  year =         "1999",
  bibdate =      "Thu Dec 20 20:22:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://groups.google.com/group/sci.crypt/browse_thread/thread/ca8682a4658a124d/",
  acknowledgement = ack-nhfb,
}

@TechReport{Marsaglia:19xx:TNP,
  author =       "George Marsaglia",
  title =        "Tables of the Normal Probability Measure of an Offset
                 Circle",
  type =         "Report",
  number =       "??",
  institution =  inst-BOEING-SRL,
  address =      inst-BOEING-SRL:adr,
  month =        "????",
  year =         "19xx",
  bibdate =      "Wed Nov 12 07:44:53 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Marsaglia:2000:ADS,
  author =       "J. C. Marsaglia and G. Marsaglia",
  title =        "The {Anderson--Darling--Savage} goddess-of-fit test",
  year =         "2000",
  bibdate =      "Tue Apr 17 07:50:11 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Unpublished. See
                 \cite{Anderson:1952:ATC,Savage:1957:ITR}.",
  acknowledgement = ack-nhfb,
  remark =       "Was this ever published? It is cited at
                 http://www.cs.hku.hk/cisc/projects/va/ and
                 www.csis.hku.hk/cisc/download/idetect/, but is not
                 found in the Elsevier or Springer databases on 17 April
                 2012, nor by three major Web engines.",
}

@TechReport{Marsaglia:2000:MRN,
  author =       "George Marsaglia",
  title =        "The Monster, a Random Number Generator with Period
                 over $ 10^{2857} $ Times as Long as the Previously
                 Touted Longest-period One",
  type =         "Technical report",
  number =       "????",
  institution =  "Florida State University",
  address =      "Tallahassee, FL, USA",
  month =        "????",
  year =         "2000",
  bibdate =      "Mon Aug 02 10:39:48 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:2000:SMG,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "A Simple Method for Generating Gamma Variables",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "363--372",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (65C60)",
  MRnumber =     "2001k:65015",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We offer a procedure for generating a gamma variate as
                 the cube of a suitably scaled normal variate. It is
                 fast and simple, assuming one has a fast way to
                 generate normal variables. In brief: generate a normal
                 variate $x$ and a uniform variate $U$ until $ \ln (U) <
                 0.5 x^2 + d - d v + d \ln (v) $, then return $ d v $.
                 Here, the gamma parameter is $ \alpha \geq 1 $, and $ v
                 = (1 + x / \sqrt {9d})^3 $ with $ d = \alpha - 1 / 3 $.
                 The efficiency is high, exceeding 0.951, 0.981, 0.992,
                 0.996 at $ \alpha = 1, 2, 4, 8 $. The procedure can be
                 made to run faster by means of a simple squeeze that
                 avoids the two logarithms most of the time; return $ d
                 v $ if $ U < 1 - 0.0331 x^4 $. We give a short C
                 program for any $ \alpha \geq 1 $, and show how to
                 boost an $ \alpha < 1 $ into an $ \alpha > 1 $. The
                 gamma procedure is particularly fast for C
                 implementation if the normal variate is generated
                 in-line, via the {\tt \#define} feature. We include
                 such an inline version, based on our ziggurat method.
                 With it, and an inline uniform generator, gamma
                 variates can be produced in 400MHz CPUs at better than
                 1.3 million per second, with the parameter $ \alpha $
                 changing from call to call.",
  accepted =     "14 Jan 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?idx=J782",
}

@Article{Marsaglia:2000:ZMG,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "The ziggurat method for generating random variables",
  journal =      j-J-STAT-SOFT,
  volume =       "5",
  number =       "8",
  pages =        "1--7",
  year =         "2000",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sun Nov 17 22:35:43 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "See \cite{Leong:2005:CIZ,Rubin:2006:EGE}.",
  URL =          "http://www.jstatsoft.org/v05/i08;
                 http://www.jstatsoft.org/v05/i08/rnorrexp.c;
                 http://www.jstatsoft.org/v05/i08/updates;
                 http://www.jstatsoft.org/v05/i08/ziggurat.pdf",
  abstract =     "We provide a new version of our ziggurat method for
                 generating a random variable from a given decreasing
                 density. It is faster and simpler than the original,
                 and will produce, for example, normal or exponential
                 variates at the rate of 15 million per second with a C
                 version on a 400MHz PC. It uses two tables, integers $
                 k_i $ and reals $ w_i $. Some 99\% of the time, the
                 required $x$ is produced by: Generate a random 32-bit
                 integer $j$ and let $i$ be the index formed from the
                 rightmost 8 bits of $j$. If $ j < k_i $ return $ x = j
                 \times w_i $.\par

                 We illustrate with C code that provides for inline
                 generation of both normal and exponential variables,
                 with a short procedure for setting up the necessary
                 tables.",
  acknowledgement = ack-nhfb,
  annote =       "This algorithm is used in Matlab's randn() function
                 for generating normally-distributed pseudo-random
                 numbers; see \cite{Moler:2001:CCN}.",
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@Unpublished{Marsaglia:2001:MOF,
  author =       "George Marsaglia",
  title =        "Memoranda to {Office of Florida State Courts
                 Administrator}",
  year =         "2001",
  bibdate =      "Wed Jun 22 07:31:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "February 5, 2001 and May 29, 2001, with
                 recommendations on jury selection.",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:2001:PUC,
  author =       "George Marsaglia",
  title =        "Problems with the Use of Computers for Selecting Jury
                 Panels",
  journal =      "Jurimetrics",
  volume =       "41",
  number =       "??",
  pages =        "425--427",
  month =        "Summer",
  year =         "2001",
  CODEN =        "JURIFF",
  ISSN =         "0897-1277",
  bibdate =      "Tue Jun 21 19:10:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://heinonline.org/HOL/Page?handle=hein.journals/juraba41&div=38&g_sent=1&collection=journals",
  acknowledgement = ack-nhfb,
}

@Misc{Marsaglia:2002:RGB,
  author =       "George Marsaglia",
  title =        "Re: *good* 64-bit random-number generator",
  howpublished = "Posting to the {\tt sci.crypt.random-numbers} news
                 group",
  day =          "3",
  month =        sep,
  year =         "2002",
  bibdate =      "Sat Mar 08 15:04:15 2008",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://groups.google.ws/group/comp.sys.sun.admin/browse_thread/thread/683ff52120e5b4d/b53ccad5aa5d6017",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:2002:SDP,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "Some Difficult-to-pass Tests of Randomness",
  journal =      j-J-STAT-SOFT,
  volume =       "7",
  number =       "3",
  pages =        "1--8",
  year =         "2002",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sun Nov 17 22:35:43 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib",
  URL =          "http://www.jstatsoft.org/v07/i03;
                 http://www.jstatsoft.org/v07/i03/tuftests.c;
                 http://www.jstatsoft.org/v07/i03/tuftests.pdf;
                 http://www.jstatsoft.org/v07/i03/updates",
  abstract =     "We describe three tests of randomness --- tests that
                 many random number generators fail. In particular, all
                 congruential generators --- even those based on a prime
                 modulus --- fail at least one of the tests, as do many
                 simple generators, such as shift register and lagged
                 Fibonacci. On the other hand, generators that pass the
                 three tests seem to pass all the tests in the Diehard
                 Battery of Tests.\par

                 Note that these tests concern the randomness of a
                 generator's output as a sequence of independent,
                 uniform 32-bit integers. For uses where the output is
                 converted to uniform variates in $ [0, 1) $, potential
                 flaws of the output as integers will seldom cause
                 problems after the conversion. Most generators seem to
                 be adequate for producing a set of uniform reals in $
                 [0, 1) $, but several important applications. notably
                 in cryptography and number theory --- for example,
                 establishing probable primes, complexity of factoring
                 algorithms, random partitions of large integers --- may
                 require satisfactory performance on the kinds of tests
                 we describe here.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@Article{Marsaglia:2003:EKD,
  author =       "George Marsaglia and Wai Wan Tsang and Jingbo Wang",
  title =        "Evaluating {Kolmogorov}'s Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "8",
  number =       "18",
  pages =        "1--4",
  year =         "2003",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Tue Dec 16 17:06:19 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstatsoft.org/v08/i18;
                 http://www.jstatsoft.org/v08/i18/k.pdf",
  abstract =     "Kolmogorov's goodness-of-fit measure, $ D_n $, for a
                 sample CDF has consistently been set aside for methods
                 such as the $ D_n^+ $ or $ D_n^- $; of Smirnov,
                 primarily, it seems, because of the difficulty of
                 computing the distribution of $ D_n $. As far as we
                 know, no easy way to compute that distribution has ever
                 been provided in the 70+ years since Kolmogorov's
                 fundamental paper. We provide one here, a C procedure
                 that provides $ \mbox {Pr}(D_n < d) $ with 13--15 digit
                 accuracy for $n$ ranging from $2$ to at least $ 16000
                 $. We assess the (rather slow) approach to limiting
                 form, and because computing time can become excessive
                 for probabilities $ > 0.999 $ with $n$'s of several
                 thousand, we provide a quick approximation that gives
                 accuracy to the 7th digit for such cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@InCollection{Marsaglia:2003:MCM,
  author =       "George Marsaglia",
  title =        "{Monte Carlo} method",
  crossref =     "Ralston:2003:ECS",
  pages =        "1192--1193",
  year =         "2003",
  bibdate =      "Wed Jun 22 06:58:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:2003:RNG,
  author =       "George Marsaglia",
  title =        "Random Number Generators",
  journal =      j-J-MOD-APPL-STAT-METH,
  volume =       "2",
  number =       "1",
  pages =        "2--13",
  month =        may,
  year =         "2003",
  CODEN =        "????",
  ISSN =         "1538-9472",
  bibdate =      "Wed Dec 17 08:26:46 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://stat.fsu.edu/pub/diehard/;
                 http://tbf.coe.wayne.edu/jmasm/;
                 http://www.csis.hku.hk/~diehard/",
  abstract =     "The author discusses some promising new random number
                 generators, as well as formulates the mathematical
                 basis that makes them random variables in the same
                 sense as more familiar ones in probability and
                 statistics, emphasizing his view that randomness exists
                 only in the sense of mathematics. He discusses the need
                 for adequate seeds that provide the axioms for that
                 mathematical basis, and gives examples from Law and
                 Gaming, where inadequacies have led to difficulties. He
                 also describes new versions of the widely used Diehard
                 Battery of Tests of Randomness.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Modern Applied Statistical Methods",
  keywords =     "Random number generator, Diehard Test",
  remark =       "This paper contains a nice survey of recommended
                 generators, a recipe for recovering the multiplier and
                 addend of linear congruential generators (p. 4,
                 ``Cracking a Congruential RNG''), information on a
                 direct floating-point RNG, and discussion of the new
                 revision of the Diehard Test Suite.",
}

@Article{Marsaglia:2003:TOS,
  author =       "George Marsaglia",
  title =        "Technical opinion: Seeds for random number generators:
                 Techniques for choosing seeds for social and scientific
                 applications of random number generators",
  journal =      j-CACM,
  volume =       "46",
  number =       "5",
  pages =        "90--93",
  month =        may,
  year =         "2003",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/769800.769827",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Sep 3 17:06:36 MDT 2003",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
}

@Article{Marsaglia:2003:XR,
  author =       "George Marsaglia",
  title =        "Xorshift {RNGs}",
  journal =      j-J-STAT-SOFT,
  volume =       "8",
  number =       "14",
  pages =        "1--6",
  year =         "2003",
  CODEN =        "JSSOBK",
  DOI =          "https://doi.org/10.18637/jss.v008.i14",
  ISSN =         "1548-7660",
  ISSN-L =       "1548-7660",
  bibdate =      "Tue Dec 16 17:06:19 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  note =         "See \cite{Brent:2004:NMX} for corrections and the
                 equivalence of xorshift generators and the
                 well-understood linear feedback shift register
                 generators. See also
                 \cite{Salmon:2011:PRN,Saito:2012:DCS,Steele:2014:FSP}
                 for the failure of Marsaglia's {\tt xorwow()} generator
                 from this paper. See
                 \cite{Panneton:2005:XRN,Vigna:2016:EEM} for detailed
                 analysis.",
  URL =          "http://www.jstatsoft.org/v08/i14;
                 http://www.jstatsoft.org/v08/i14/xorshift.pdf",
  abstract =     "Description of a class of simple, extremely fast
                 random number generators (RNGs) with periods $ 2^k - 1
                 $ for $ k = 32, 64, 96, 128, 160, 192 $. These RNGs
                 seem to pass tests of randomness very well.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@Article{Brent:2004:NMX,
  author =       "Richard P. Brent",
  title =        "Note on {Marsaglia}'s Xorshift Random Number
                 Generators",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "5",
  pages =        "1--5",
  year =         "2004",
  CODEN =        "JSSOBK",
  DOI =          "https://doi.org/10.18637/jss.v011.i05",
  ISSN =         "1548-7660",
  ISSN-L =       "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  note =         "See
                 \cite{Marsaglia:2003:XR,Panneton:2005:XRN,Vigna:2016:EEM}.
                 This article shows the equivalence of xorshift
                 generators and the well-understood linear feedback
                 shift register generators.",
  URL =          "http://www.jstatsoft.org/counter.php?id=101&url=v11/i05/v11i05.pdf&ct=1",
  accepted =     "2004-08-25",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  submitted =    "2004-07-07",
}

@Article{Marsaglia:2004:BURa,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "The 64-bit universal {RNG}",
  journal =      j-STAT-PROB-LETT,
  volume =       "66",
  number =       "2",
  pages =        "183--187",
  year =         "2004",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2003.11.001",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65C10",
  MRnumber =     "2 029 733",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 MathSciNet database",
  URL =          "http://www.doornik.com/research/randomdouble.pdf",
  ZMnumber =     "02041513",
  abstract =     "We describe a random number generator that produces
                 uniform $ [0, 1) $ variates directly, as 64-bit
                 floating point numbers, without the customary floating
                 of integers. Using only subtraction and tests on
                 magnitude, the method is readily implemented and
                 should, given the same seed values, produce exactly the
                 same random numbers with most programming languages.
                 The resulting numbers have a very long period ($
                 \approx 2^{202} $ or $ 10^{61} $ ) and apparently
                 excellent randomness---supported by extensive
                 testing.",
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "64-bit floating point; Random number generators;
                 Seeds",
  ZMclass =      "*62-99 Statistics",
}

@Article{Marsaglia:2004:EAD,
  author =       "George Marsaglia and John Marsaglia",
  title =        "Evaluating the {Anderson--Darling} Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "9",
  number =       "2",
  pages =        "1--5",
  day =          "25",
  month =        feb,
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Wed Feb 25 11:20:56 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib",
  URL =          "http://www.jstatsoft.org/v09/i02/ad.pdf;
                 http://www.jstatsoft.org/v09/i02/ADinf.c;
                 http://www.jstatsoft.org/v09/i02/AnDarl.c",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
}

@Article{Marsaglia:2004:END,
  author =       "George Marsaglia",
  title =        "Evaluating the Normal Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "4",
  pages =        "1--7",
  month =        "????",
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1",
  accepted =     "2004-07-18",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  remark =       "This article exhibits accurate, compact, and fast
                 algorithms for computation of the normal distribution
                 function and the complementary normal distribution,
                 which have a simple relation to the error function and
                 the complementary error function. They appear to be
                 improvements on almost all previously-published
                 algorithms for these functions. However, closer study
                 shows that the complementary normal distribution
                 function has an unchecked out-of-bounds array access
                 for |x| >= 17, and its Taylor series sum has poor
                 convergence because the tabulated intervals are twice
                 too wide. The Taylor series sum for the normal
                 distribution function is expanded around x = 0, and
                 thus has poor convergence for large |x|. Neither
                 function takes into account the accuracy loss when the
                 computed result is the larger of the two (their sum is
                 one, and their range is [-Infinity,+Infinity]),
                 although the text discusses the problem. The article
                 also discusses the historical origin of the term
                 ``error function'', tracing it to J. W. Glaisher in
                 1871.",
  submitted =    "2004-06-05",
}

@Article{Marsaglia:2004:FGD,
  author =       "George Marsaglia and Wai Wan Tsang and Jingbo Wang",
  title =        "Fast Generation of Discrete Random Variables",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "3",
  pages =        "1--8",
  month =        "????",
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstatsoft.org/counter.php?id=99&url=v11/i03/discrete.pdf&ct=1",
  accepted =     "2004-07-12",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  submitted =    "2004-06-05",
  xxpages =      "1--11",
}

@Article{Marsaglia:2005:MGF,
  author =       "George Marsaglia",
  title =        "Monkeying with the Goodness-of-Fit Test",
  journal =      j-J-STAT-SOFT,
  volume =       "14",
  number =       "13",
  pages =        "1--4",
  day =          "20",
  month =        sep,
  year =         "2005",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Mon Dec 12 11:09:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstatsoft.org/counter.php?id=138&url=v14/i13&ct=2;
                 http://www.jstatsoft.org/counter.php?id=138&url=v14/i13/v14i13.pdf&ct=1",
  abstract =     "The familiar $ \sumP (\textrm {OBS} - \textrm {EXP})^2
                 / \textrm {EXP} $ goodness-of-fit measure is commonly
                 used to test whether an observed sequence came from the
                 realization of $n$ independent identically distributed
                 (iid) discrete random variables. It can be quite
                 effective for testing for identical distribution, but
                 is not suited for assessing independence, as it pays no
                 attention to the order in which output values are
                 received.\par

                 This note reviews a way to adjust or tamper, that is,
                 monkey-with the classical test to make it test for
                 independence as well as identical distribution in
                 short, to test for both the i's in iid, using monkey
                 tests similar to those in the Diehard Battery of Tests
                 of Randomness (Marsaglia 1995).",
  accepted =     "2005-09-20",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  keywords =     "$\chi^2$; goodness of fit; monkey tests; overlapping
                 m-tuples",
  submitted =    "2005-05-01",
}

@Article{Marsaglia:2005:RPO,
  author =       "George Marsaglia",
  title =        "On the Randomness of Pi and Other Decimal Expansions",
  journal =      "{InterStat}: statistics on the {Internet}",
  pages =        "17",
  month =        oct,
  year =         "2005",
  CODEN =        "????",
  ISSN =         "1941-689X",
  bibdate =      "Wed Jun 22 10:34:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://yaroslavvb.com/papers/marsaglia-on.pdf;
                 https://web.archive.org/web/20060827003645/http://interstat.statjournals.net/INDEX/Oct05.html;
                 https://web.archive.org/web/20061002145157/http://interstat.statjournals.net/YEAR/2005/abstracts/0510005.php;
                 https://web.archive.org/web/20061116062707/http://interstat.statjournals.net/YEAR/2005/articles/0510005.pdf",
  abstract =     "Tests of randomness much more rigorous than the usual
                 frequency-of-digit counts are applied to the decimal
                 expansions of $ \pi $, $e$ and $ \sqrt {2} $, using the
                 Diehard Battery of Tests adapted to base 10 rather than
                 the original base 2. The first $ 10^9 $ digits of $ \pi
                 $, $e$ and $ \sqrt {2} $ seem to pass the Diehard tests
                 very well. But so do the decimal expansions of most
                 rationals $ k / p $ with large primes $p$. Over the
                 entire set of tests, only the digits of $ \sqrt {2} $
                 give a questionable result: the monkey test on 5-letter
                 words. Its significance is discussed in the
                 text.\par

                 Three specific $ k / p $ are used for comparison. The
                 cycles in their decimal expansions are developed in
                 reverse order by the multiply-with-carry (MWC) method.
                 They do well in the Diehard tests, as do many fast and
                 simple MWC RNGs that produce base-$b$ `digits' of the
                 expansions of $ k / p $ for $ b = 2^{32} $ or $ b =
                 2^{32} - 1 $. Choices of primes $p$ for such MWC RNGs
                 are discussed, along with comments on their
                 implementation.",
  abstract-2 =   "Extensive tests of randomness used to distinguish good
                 from not-so-good random number generators are applied
                 to the digits of $\pi$, $e$ and $\sqrt{2}$, as well as
                 to rationals $k / p$ for large primes $p$. They seem to
                 pass these tests as well as some of the best RNGs, and
                 could well serve in their stead if the digits could be
                 easily and quickly produced in the computer---and they
                 can, at least for rationals $k / p$. Simple and fast
                 methods are developed to produce, in reverse order, for
                 large primes $p$ and general bases $b$, the periodic
                 cycles of the base-$b$ expansions of $k / p$. Specific
                 choices provide high quality, fast and simple RNGs with
                 periods thousands of orders of magnitude greater than
                 what are currently viewed as the longest. Also included
                 are historical references to decimal expansions and
                 their relation to current, often wrong, website
                 discussions on the randomness of $\pi$.",
  acknowledgement = ack-nhfb,
  keywords =     "Diehard Tests; Pi; Random Number Generators; Tests of
                 Randomness",
  remark =       "The statjournals.net domain has been taken over by a
                 malicious owner, but the original Web pages and PDF
                 file have been recovered at other locations listed in
                 the URL value. The marsaglia-on.pdf file from that
                 location has been verified to be identical to a file
                 independently downloaded at Utah on 22-Jun-2011, with
                 MD5 checksum 1558dafb9bbcdcecdd656d155bac22f1 and
                 created by MiKTeX pdfTeX-1.21a on Fri Oct 28 15:35:33
                 2005.",
  xxURL =        "http://interstat.statjournals.net/INDEX/Oct05.html;
                 http://interstat.statjournals.net/YEAR/2005/articles/0510005.pdf",
}

@Article{Marsaglia:2006:RCS,
  author =       "George Marsaglia",
  title =        "Refutation of claims such as {``Pi is less random than
                 we thought''}",
  journal =      "{InterStat}: statistics on the {Internet}",
  pages =        "5",
  day =          "23",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "1941-689X",
  bibdate =      "Tue Jun 21 19:08:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://yaroslavvb.com/papers/marsaglia-refutation.pdf",
  abstract =     "In article by Tu and Fischman in a Physics journal
                 \cite{Tu:2005:SRD} has led to worldwide reports that Pi
                 is less random than we thought, or that Pi is not the
                 best random number generator, or that Pi seems good but
                 not the best. A careful examination of the Tu and
                 Fischman procedure shows that it is needlessly
                 complicated and can be reduced to study of the average
                 value of $ (U_2 - U_1) (U_2 - U_3) $ for uniform
                 variates U produced by a RNG, (but not on their
                 distribution). The authors' method of assigning a
                 letter grade, A+, A, B, C, D, E to a sample mean, based
                 on its distance from the expected value, suggests
                 naivety in the extreme. Application, in the present
                 article, to the first 960 million digits of the
                 expansion of Pi shows that they perform as well as
                 other RNGs on not only the average for $ (U_2 - U_1)
                 (U_2 - U_3) $, but on the more difficult test for their
                 distribution, consistent with results previously shown
                 in this journal that Pi does quite well on far more
                 extensive and difficult-to-pass tests of randomness.",
  acknowledgement = ack-nhfb,
  keywords =     "Diehard Tests; LSTests of Randomness; Pi; Random
                 Number Generators",
  remark =       "The statjournals.net domain has been taken over by a
                 malicious owner, but the PDF file has been recovered at
                 another location listed in the URL value, and verified
                 to be identical to a copy independently downloaded at
                 Utah on 22-Jun-2011, with MD5 checksum
                 66b28f8a65a37d19d262d42d38ca676f and created by MiKTeX
                 pdfTeX-1.21a on Mon Jan 23 07:14:22 2006.",
  xxURL =        "http://interstat.statjournals.net/YEAR/2006/articles/0601001.pdf",
}

@Article{Marsaglia:2006:RNV,
  author =       "George Marsaglia",
  title =        "Ratios of Normal Variables",
  journal =      j-J-STAT-SOFT,
  volume =       "16",
  number =       "4",
  pages =        "1--10",
  month =        may,
  year =         "2006",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Fri Jul 4 10:54:15 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.jstatsoft.org/v16/i04",
  abstract =     "This article extends and amplifies on results from a
                 paper of over forty years ago. It provides software for
                 evaluating the density and distribution functions of
                 the ratio $ z / w $ for any two jointly normal variates
                 $z$, $w$, and provides details on methods for
                 transforming a general ratio $ z / w $ into a standard
                 form, $ (a + x) / (b + y) $, with $x$ and $y$
                 independent standard normal and $a$, $b$ non-negative
                 constants. It discusses handling general ratios when,
                 in theory, none of the moments exist yet practical
                 considerations suggest there should be approximations
                 whose adequacy can be verified by means of the included
                 software. These approximations show that many of the
                 ratios of normal variates encountered in practice can
                 themselves be taken as normally distributed. A
                 practical rule is developed: If $ a < 2.256 $ and $ 4 <
                 b $ then the ratio $ (a + x) / (b + y) $ is itself
                 approximately normally distributed with mean $ \mu = a
                 / (1.01 b - 0.2713) $ and variance $ \sigma^2 = (a^2 +
                 1) / (b^2 + 0.108 b - 3.795) \mu^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  pubdates =     "Submitted 2006-03-07; Accepted 2006-05-11",
}

@Misc{Marsaglia:2010:SKR,
  author =       "George Marsaglia",
  title =        "{SUPER KISS} random-number generator",
  howpublished = "Web posting",
  day =          "3",
  month =        nov,
  year =         "2010",
  bibdate =      "Mon Dec 31 17:17:20 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.velocityreviews.com/forums/t704080-re-rngs-a-super-kiss.html",
  acknowledgement = ack-nhfb,
  remark =       "This note introduces source code for an extension of
                 the KISS generator Marsaglia:1993:KG that combines it
                 with others to produce a generator with a period of $
                 54767 \times 2^{1337279} \approx 10^{402 \, 565} $.",
}

@Misc{Marsaglia:2011:RPE,
  author =       "George Marsaglia",
  title =        "{RNGs} with periods exceeding $ 10^{\hbox {40
                 million}} $",
  howpublished = "Message-ID {\tt
                 <603ebe15-a32f-4fbb-ba44-6c73f7919a33@t35g2000yqj.googlegroups.com>}
                 in newsgroups {\tt sci.math}, {\tt comp.lang.c} and
                 {\tt sci.crypt}.",
  day =          "16",
  month =        jan,
  year =         "2011",
  bibdate =      "Wed Jun 22 18:06:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

%%% ====================================================================
%%% Papers cross-referenced by Marsaglia bibliography entries, or
%%% citing Marsaglia in their titles:

@Article{Anderson:1952:ATC,
  author =       "T. W. Anderson and D. A. Darling",
  title =        "Asymptotic theory of certain `goodness of fit'
                 criteria based on stochastic processes",
  journal =      j-ANN-MATH-STAT,
  volume =       "23",
  number =       "2",
  pages =        "193--212",
  month =        jun,
  year =         "1952",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  bibdate =      "Tue Apr 17 07:38:55 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.jstor.org/stable/2236446",
  abstract =     "The statistical problem treated is that of testing the
                 hypothesis that $n$ independent, identically
                 distributed random variables have a specified
                 continuous distribution function $ F(x) $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
}

@Article{Savage:1957:ITR,
  author =       "Richard Savage",
  title =        "On the Independence of Tests of Randomness and Other
                 Hypotheses",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "52",
  number =       "277",
  pages =        "53--57",
  month =        mar,
  year =         "1957",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:32 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314156;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.jstor.org/stable/2281400",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Coveyou:1967:FAU,
  author =       "R. R. Coveyou and R. D. MacPherson",
  title =        "{Fourier} Analysis of Uniform Random Number
                 Generators",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "1",
  pages =        "100--119",
  month =        jan,
  year =         "1967",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  annote =       "A method of analysis of uniform random number
                 generators is developed, applicable to almost all
                 practical methods of generation. The method is that of
                 Fourier analysis of the output sequences of such
                 generators. With this tool it is possible to understand
                 and predict relevant statistical properties of such
                 generators and compare and evaluate such methods. Many
                 such analyses and comparisons have been carried out.",
  descriptors =  "Shift register sequences; method; spectral analysis;
                 interdependence; multidimensional uniformity; RNG;
                 test",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{VanGelder:1967:SNR,
  author =       "A. {Van Gelder}",
  title =        "Some New Results in Pseudo-Random Number Generation",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "4",
  pages =        "785--792",
  month =        oct,
  year =         "1967",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321420.321437",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 1 09:50:45 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  abstract =     "Pseudo-random number generators of the power residue
                 (sometimes called congruential or multiplicative) type
                 are discussed and results of statistical tests
                 performed on specific examples of this type are
                 presented. Tests were patterned after the methods of
                 MacLaren and Marsaglia (M\&M). The main result
                 presented is the discovery of several power residue
                 generators which performed well in these tests. This is
                 important because, of all the generators using standard
                 methods (including power residue) that were tested by
                 M\&M, none gave satisfactory results. The overall
                 results here provide further evidence for their
                 conclusion that the types of tests usually encountered
                 in the literature do not provide an adequate index of
                 the behavior of n-tuples of consecutively generated
                 numbers. In any Monte Carlo or simulation problem where
                 n supposedly independent random numbers are required at
                 each step, this behavior is likely to be important.
                 Finally, since the tests presented here differ in
                 certain details from those of M\&M, some of their
                 generators were retested as a check. A cross-check
                 shows that results are compatible; in particular, if a
                 generator failed one of their tests badly, it also
                 failed the present author's corresponding test badly.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Westlake:1967:URN,
  author =       "W. J. Westlake",
  title =        "A Uniform Random Number Generator Based on the
                 Combination of Two Congruential Generators",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "2",
  pages =        "337--340",
  month =        apr,
  year =         "1967",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321386.321396",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Dec 22 07:42:23 2011",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  abstract =     "A method of generating pseudo-random uniform numbers
                 based on the combination of two congruential generators
                 is described. It retains two of the desirable features
                 of congruential generators, namely, the long cycle and
                 the case of implementation on a digital computer.
                 Furthermore, unlike the method of combining
                 congruential generators recently proposed by MacLaren
                 and Marsaglia, it does not require the retention in
                 computer memory of a table of generated numbers. The
                 generator gave completely satisfactory results on a
                 fairly stringent series of statistical tests.",
  acknowledgement = ack-nhfb,
  descriptors =  "RNG",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Whittlesey:1969:LEM,
  author =       "John R. B. Whittlesey",
  title =        "Letter to the {Editor}: {On} the Multidimensional
                 Uniformity of Pseudorandom Generators",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "247--247",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
  note =         "See \cite{Marsaglia:1968:RNF}.",
  acknowledgement = ack-nhfb,
  annote =       "It would appear that George Marsaglia's recent article
                 proving that all the pseudorandom points generated in
                 the unit n-cube ``will be found to lie in a relatively
                 small number of parallel hyperplanes'' has given the
                 coup de grace, to the use of multiplicative
                 congruential generators in all Monte Carlo
                 applications, except those having the most
                 non-stringent requirements for multidimensional
                 uniformity.",
  country =      "USA",
  descriptors =  "Comparison; shift register sequences; Tausworthe
                 generator; RNG; test; multidimensional uniformity; grid
                 structure; linear congruential generator",
  enum =         "3286",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "PRNG (pseudo-random number generator)",
  references =   "7",
}

@Article{Pokhodzei:1983:OMM,
  author =       "B. B. Pokhodze{\u\i}",
  title =        "Optimality of the {Marsaglia} method for simulating
                 discrete distributions",
  journal =      "Vestnik Leningrad. Univ. Mat. Mekh. Astronom.",
  volume =       "4",
  pages =        "105--107",
  year =         "1983",
  CODEN =        "VMMAA3",
  ISSN =         "0024-0850",
  MRclass =      "65C10",
  MRnumber =     "85a:65015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0551.60020",
  abstract =     "It is shown that after a small modification the famous
                 {\it G. Marsaglia's} method [Commun. ACM 6, 37-38
                 (1963; Zbl 0112.084)] for generation of discrete
                 distributions reduces to an optimal algorithm for
                 transformation of random bits to random variables with
                 given distribution.",
  classmath =    "*60E99 Distribution theory in probability theory 65C10
                 Random number generation",
  fjournal =     "Vestnik Leningradskogo Universiteta, Seriya 1:
                 Matematika, Mekhanika, Astronomiya",
  keywords =     "Marsaglia's method; transformation of random bits to
                 random variables with given distribution",
  language =     "Russian. English summary",
  xxtitle =      "On optimal {Marsaglia}'s method for simulating
                 discrete distributions",
}

@Article{Retter:1984:CMM,
  author =       "C. Retter",
  title =        "Cryptanalysis of a {Maclaren--Marsaglia} System",
  journal =      j-CRYPTOLOGIA,
  volume =       "8",
  number =       "2",
  pages =        "97--108",
  month =        apr,
  year =         "1984",
  CODEN =        "CRYPE6",
  ISSN =         "0161-1194 (print), 1558-1586 (electronic)",
  ISSN-L =       "0161-1194",
  bibdate =      "Sat Nov 21 12:35:16 MST 1998",
  bibsource =    "http://www.dean.usma.edu/math/pubs/cryptologia/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
  note =         "See also letters and responses, Cryptologia {\bf 8},
                 1984, pp. 374--378.",
  acknowledgement = ack-nhfb,
  fjournal =     "Cryptologia",
  journal-URL =  "http://www.tandfonline.com/loi/ucry20",
  romanvolume =  "VIII",
}

@Article{Retter:1985:KSA,
  author =       "C. Retter",
  title =        "Key-Search Attack on {Maclaren--Marsaglia} Systems",
  journal =      j-CRYPTOLOGIA,
  volume =       "9",
  number =       "2",
  pages =        "114--130",
  month =        apr,
  year =         "1985",
  CODEN =        "CRYPE6",
  ISSN =         "0161-1194 (print), 1558-1586 (electronic)",
  ISSN-L =       "0161-1194",
  bibdate =      "Sat Nov 21 12:35:16 MST 1998",
  bibsource =    "http://www.dean.usma.edu/math/pubs/cryptologia/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Cryptologia",
  journal-URL =  "http://www.tandfonline.com/loi/ucry20",
  romanvolume =  "IX",
}

@Article{Eichenauer:1988:MLTb,
  author =       "J{\"u}rgen Eichenauer and Harald Niederreiter",
  title =        "On {Marsaglia}'s lattice test for pseudorandom
                 numbers",
  journal =      j-MANUSCR-MATH,
  volume =       "62",
  number =       "2",
  pages =        "245--248",
  year =         "1988",
  CODEN =        "MSMHB2",
  ISSN =         "0025-2611 (print), 1432-1785 (electronic)",
  ISSN-L =       "0025-2611",
  MRclass =      "65C10 (11K45)",
  MRnumber =     "90c:65011",
  MRreviewer =   "J. Patrick Lambert",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0663.65006",
  abstract =     "Nonlinear recursive congruential pseudorandom number
                 equations with prime modulus and maximal period length
                 are considered. The authors give characterizations for
                 these generator which behave optimally with respect to
                 Marsaglia's lattice test.",
  classmath =    "*65C10 Random number generation; 11K99 Probabilistic
                 theory",
  fjournal =     "Manuscripta Mathematica",
  keywords =     "Marsaglia's lattice test; maximal period length;
                 Nonlinear recursive congruential pseudorandom number
                 equations",
  ZMreviewer =   "R. F. Tichy",
}

@Article{Eichenauer:1988:MLTc,
  author =       "J{\"u}rgen Eichenauer and Holger Grothe and J{\"u}rgen
                 Lehn",
  title =        "{Marsaglia}'s lattice test and non-linear congruential
                 pseudo-random number generators",
  journal =      j-METRIKA,
  volume =       "35",
  number =       "3/4",
  pages =        "241--250",
  year =         "1988",
  CODEN =        "MTRKA8",
  ISSN =         "0026-1335 (print), 1435-926X (electronic)",
  ISSN-L =       "0026-1335",
  MRclass =      "65C10",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0653.65006",
  abstract =     "A recursive congruential non-additive generator of the
                 form $ (1) \quad x_{n + 1} \equiv f(x_n)(m o d p), $ $
                 x_{n + 1} \in {\bbfZ }_p $, $ n \ge 0 $, is considered,
                 where p is a large prime number, $ {\bbfZ }_p = \{ 0,
                 1, ..., p - 1 \} $, $ x_0 \in {\bbfZ }_p $, and f: $
                 {\bbfZ }_p \to {\bbfZ }_p $ is a function such that (1)
                 has maximal period length. The sequences of integers $
                 \{ x_i : $ $ i \ge 0 \} $ generated by (1) are divided
                 into vectors of $ d \ge 2 $ consecutive numbers: $
                 v^d_i = (x_i, ..., x_{i + d - 1})^T \in {\bbfZ }^d_p $
                 and let $ w^d_i \equiv v_i^d - v^d_0 (m o d p), $ $ i
                 \ge 0 $. For $ d \le 3 $, it is shown that $ V^d =
                 {\bbfZ }^d_p, $ where $ V^d = \{ v \in {\bbfZ }^d_p
                 \vert \quad v \equiv \sum^{p - 1}_{i = 1z}_i w^d_i (m o
                 d p); \quad z_1, ..., z_{p - 1} \in {\bbfZ }_p \} . $
                 In other words, (1) passes {\it G. Marsaglia}'s lattice
                 test [Applications of number theory to numerical
                 analysis, 249-285 (1972; Zbl 0266.65007)]. For $ d \ge
                 4 $ there are generators (1) which fail this test. It
                 is also shown that the generators of a class of
                 nonlinear generators introduced by the first and the
                 third author [Stat. Hefte 27, 315-326 (1986; Zbl
                 0607.65001)] pass Marsaglia's lattice test for $ d \le
                 (p - 1) / 2 $.",
  classmath =    "*65C10 Random number generation",
  fjournal =     "Metrika. International Journal for Theoretical and
                 Applied Statistics",
  journal-URL =  "http://link.springer.com/journal/184",
  keywords =     "Marsaglia's lattice test; nonlinear generators; pseudo
                 random number generators; recursive congruential
                 non-additive generator",
  ZMreviewer =   "R. Theodorescu",
}

@Article{Harmon:1988:AIM,
  author =       "Marion G. Harmon and Ted P. Baker",
  title =        "An {Ada} Implementation of {Marsaglia}'s ``Universal''
                 Random Number Generator",
  journal =      j-SIGADA-LETTERS,
  volume =       "8",
  number =       "2",
  pages =        "110--112",
  month =        mar # "\slash " # apr,
  year =         "1988",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:28 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGADA Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "algorithms; design; languages; real numbers; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada \\ G.3 Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Random number generation",
}

@Article{Ferrenberg:1992:MCS,
  author =       "A. M. Ferrenberg and D. P. Landau and Y. J. Wong",
  title =        "{Monte Carlo} simulations: Hidden errors from `good'
                 random number generators",
  journal =      j-PHYS-REV-LET,
  volume =       "69",
  number =       "23",
  pages =        "3382--3384",
  day =          "7",
  month =        dec,
  year =         "1992",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.69.3382",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sun Dec 18 09:16:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "See also \cite{Grassberger:1993:CGR}.",
  URL =          "http://prl.aps.org/abstract/PRL/v69/i23/p3382_1",
  abstract =     "The Wolff algorithm is now accepted as the best
                 cluster-flipping Monte Carlo algorithm for beating
                 ``critical slowing down.'' We show how this method can
                 yield incorrect answers due to subtle correlations in
                 ``high quality'' random number generators.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  remark =       "This paper is cited for its revelations about the
                 sensitivity of Monte Carlo simulations to the
                 underlying random-number generator. From the paper:\par
                 Page 3383: ``Surprisingly, we find that the use of the
                 `high quality' generators together with the Wolff
                 algorithm produces systematically incorrect results.
                 \ldots{} Runs made using the SWC generator gave better
                 results, but even these data showed noticeable
                 systematic errors which had the opposite sign from
                 those produced using R250. In contrast, data obtained
                 using the simple 32-bit congruential generator CONG
                 produced answers which were correct to within the error
                 bars. Even use of the mixed generator SWCW did not
                 yield results which were free of bais, although the
                 systematic errors were much smaller.''\par From page
                 3384: ``extensive Monte Carlo simulations on an Ising
                 model for which the exact answers are known have shown
                 that ostensibly high quality random number generators
                 may lead to subtle, but dramatic, systematic errors for
                 some algorithms, but not others. Since there is no
                 reason to believe that the model which we have
                 investigated has any special idiosyncrasies, these
                 results offer another stern warning about the need to
                 very carefully test the implementation of new
                 algorithms. In particular, this means that a specific
                 algorithm must be tested together with the random
                 number generator being used {\em regardless} of the
                 tests which the generator has passed.''",
  remark-corr =  "See \cite{Kalle:1984:PRN, Berdnicov:1991:MCS,
                 Ferrenberg:1992:MCS, Grassberger:1993:CGR,
                 Kankaala:1993:BLC, Selke:1993:CFM, Coddington:1994:ARN,
                 Holian:1994:PNG, Vattulainen:1994:PTR,
                 Compagner:1995:OCR, Schmid:1995:EMC,
                 Vattulainen:1995:CSS, Vattulainen:1995:PMT,
                 Bromley:1996:QNG, Coddington:1997:RNG, Shchur:1997:CMC,
                 Shchur:1997:SDR, DSouza:1998:SBD, Gammel:1998:HRR,
                 Resende:1998:URN, Mertens:2003:EPR, Bauke:2004:PRC,
                 Mertens:2004:EPR, Ossola:2004:SED} for examples of
                 generator correlations causing Monte Carlo simulations
                 in physics to converge to the wrong answer.",
}

@Article{Peterson:1992:MCP,
  author =       "I. Peterson",
  title =        "{Monte Carlo} Physics: {A} Cautionary Lesson",
  journal =      j-SCIENCE-NEWS,
  volume =       "142",
  number =       "25--26",
  pages =        "422--422",
  day =          "19",
  month =        dec,
  year =         "1992",
  CODEN =        "SCNEBK",
  ISSN =         "0036-8423 (print), 1943-0930 (electronic)",
  ISSN-L =       "0036-8423",
  bibdate =      "Sat Mar 03 07:52:46 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Comment on negative experience with the
                 Marsaglia--Zaman generator reported in
                 \cite{Ferrenberg:1992:MCS}. See response
                 \cite{Marsaglia:1993:LHR}.",
  URL =          "http://www.jstor.org/stable/4018020",
  acknowledgement = ack-nhfb,
  ajournal =     "Sci. News (Washington, DC)",
  fjournal =     "Science News (Washington, DC)",
  journal-URL =  "http://www.jstor.org/journals/00368423.html;
                 http://www.sciencenews.org/view/archives;
                 http://www3.interscience.wiley.com/journal/122396840/home",
}

@Article{Percus:1995:TAM,
  author =       "Ora E. Percus and Paula A. Whitlock",
  title =        "Theory and application of {Marsaglia}'s monkey test
                 for pseudorandom number generators",
  journal =      j-TOMACS,
  volume =       "5",
  number =       "2",
  pages =        "87--100",
  month =        apr,
  year =         "1995",
  CODEN =        "ATMCEZ",
  DOI =          "https://doi.org/10.1145/210330.210331",
  ISSN =         "1049-3301 (print), 1558-1195 (electronic)",
  ISSN-L =       "1049-3301",
  bibdate =      "Thu Aug 7 12:05:30 MDT 2003",
  bibsource =    "http://dblp.uni-trier.de/db/journals/tomacs/tomacs5.html#PercusW95;
                 http://www.acm.org/pubs/contents/journals/tomacs/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  note =         "See \cite{Marsaglia:1993:MTR}.",
  ZMnumber =     "0853.65009",
  abstract-1 =   "A theoretical analysis is given for a new test, the
                 ``Monkey'' test, for pseudorandom number sequences,
                 which was proposed by Marsaglia. Selected results,
                 using the test on several pseudorandom number
                 generators in the literature, are also presented.",
  abstract-2 =   "The authors give a survey on theory and application of
                 Marsaglia's monkey test for pseudo-random number
                 generators. The aim of the test is to find out
                 correlations between small subsequences of the full
                 sequence of a pseudorandom number generator. For
                 illustration, the test is used to investigate five
                 known pseudorandom number generators.",
  acknowledgement = ack-nhfb,
  classmath =    "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  fjournal =     "ACM Transactions on Modeling and Computer Simulation",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J781",
  keywords =     "empirical tests; Marsaglia's monkey test; pseudorandom
                 number generators",
  oldlabel =     "PercusW95",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/tomacs/PercusW95",
  ZMreviewer =   "B. Mathiszik (Halle)",
}

@Article{Dyadkin:1997:FEL,
  author =       "Iosif G. Dyadkin and Kenneth G. Hamilton",
  title =        "A family of enhanced {Lehmer} random number
                 generators, with hyperplane suppression, and direct
                 support for certain physical applications",
  journal =      j-COMP-PHYS-COMM,
  volume =       "107",
  number =       "1--3",
  pages =        "258--280",
  day =          "22",
  month =        dec,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00101-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65C10 86-08 86A20",
  bibdate =      "Thu Nov 14 10:49:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
  URL =          "http://www.cpc.cs.qub.ac.uk/cpc/;
                 http://www.cpc.cs.qub.ac.uk/cpc/cgi-bin/list_summary.pl?CatNumber=ADGW",
  ZMnumber =     "0938.65006",
  abstract =     "Over two hundred congruential pseudorandom number
                 generators, each with a different multiplier, are built
                 into a single assembler routine that returns 32-bit
                 integer and floating-point values. This gives a Monte
                 Carlo user the opportunity of selecting a combination
                 of sequences, so as to provide a greater appearance of
                 chaos. The software makes use of extended 64-bit
                 arithmetic on Intel 386/387 (or higher) chips, thus
                 attaining a period of 262 for each of the individual
                 generators. The routine also features entry points that
                 more directly support certain applications, such as
                 well logging in nuclear geophysics. In addition to the
                 customary uniform (0,1) ``white noise'' generator, the
                 package provides values distributed according to the
                 exponential and Gaussian distributions, random unit
                 vectors in two and three dimensions, as well as
                 Klein--Nishina and neutron scattering distributions.",
  acknowledgement = ack-nhfb,
  annote =       "This paper describes a Fortran-callable Intel IA-32
                 assembly language implementation of a family of 200
                 pseudo-random number generators, based on earlier work
                 \cite{Dyadkin:1997:SBM}, with associated routines for
                 generating several distributions (uniform, exponential,
                 Gaussian, 2-D and 3-D unit vectors, plus several
                 specific to physics applications). It contains a good
                 discussion of randomness-testing procedures, and
                 comparisons with other algorithms, including the
                 ziggurat method
                 \cite{Marsaglia:1984:FEI,Marsaglia:2000:ZMG} used in
                 Matlab version 5 and later \cite{Moler:2001:CCN}. The
                 software is available from the CPC Library, for a fee,
                 and with use restrictions.",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "RNLEHMER200 (Intel IA-32 assembly language, 4044
                 Lines)",
}

@Article{Dyadkin:1997:SBM,
  author =       "Iosif G. Dyadkin and Kenneth G. Hamilton",
  title =        "A study of $ 64 $-bit multipliers for {Lehmer}
                 pseudorandom number generators",
  journal =      j-COMP-PHYS-COMM,
  volume =       "103",
  number =       "2--3",
  pages =        "103--130",
  month =        jul,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00052-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65C10",
  MRnumber =     "98f:65013",
  bibdate =      "Thu Nov 14 11:03:33 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
  ZMnumber =     "0980.65007",
  abstract =     "A study was conducted of multipliers for 64-bit
                 congruential pseudorandom number generators. Extensive
                 analysis and testing resulted in the identification of
                 over $ 200 $ good multipliers of the form $ A = 5^k $,
                 where $k$ is a prime number. The integer lattice
                 structure from any single multiplier is so fine that it
                 is not visible when {\tt REAL*4} values are returned in
                 up to four dimensions. Known number-theoretic
                 characteristics of $ m = 2^l $ generators were
                 exploited to provide a remarkably sensitive new lattice
                 test, one that is based on analysis of spacings in
                 several dimensions. That examination led to new methods
                 that can provide lattice-free pseudorandom streams in
                 up to 200 dimensions, and with extended period
                 length.",
  acknowledgement = ack-nhfb,
  annote =       "This is the theoretical work behind the software
                 \cite{Dyadkin:1997:FEL}. The linear-congruential
                 generators have multipliers of the form $ A = 5^k \bmod
                 2^{64} $, where $k$ is a prime number, and testing has
                 identified more than 200 suitable values of $k$. This
                 work was later updated for 128-bit arithmetic
                 \cite{Dyadkin:2000:SBM}.",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Bach:1998:EPM,
  author =       "Eric Bach",
  title =        "Efficient prediction of {Marsaglia--Zaman} random
                 number generators",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "44",
  number =       "3",
  pages =        "1253--1257",
  year =         "1998",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.669305",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  MRclass =      "65C10",
  MRnumber =     "99b:65007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  ZMnumber =     "0915.65003",
  abstract =     "This paper presents two properties of the random
                 number generator by {\it G. Marsaglia} and {\it A.
                 Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
                 0733.65005)]. First, it is shown that its successive
                 digits are digits of certain rational $b$-adic numbers.
                 Then, an efficient algorithm is derived to predict an
                 unknown pseudorandom sequence of this type. Two
                 examples of the prediction are given.",
  classmath =    "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  fjournal =     "Institute of Electrical and Electronics Engineers.
                 Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  keywords =     "$b$-adic number; algorithm; continued fraction;
                 pseudo-random number generator",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@Book{Robert:1999:MCS,
  author =       "Christian P. Robert and George Casella",
  title =        "{Monte Carlo} statistical methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxi + 507",
  year =         "1999",
  ISBN =         "0-387-98707-X",
  ISBN-13 =      "978-0-387-98707-1",
  LCCN =         "QA276 .R575 1999",
  bibdate =      "Wed Jun 22 08:52:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Springer texts in statistics",
  acknowledgement = ack-nhfb,
  remark =       "Section 2.1.2 gives a description of the
                 Marsaglia\slash Zaman KISS generator.",
  subject =      "Mathematical statistics; Monte Carlo method",
}

@Article{Dyadkin:2000:SBM,
  author =       "Iosif G. Dyadkin and Kenneth G. Hamilton",
  title =        "A study of 128-bit multipliers for congruential
                 pseudorandom number generators",
  journal =      j-COMP-PHYS-COMM,
  volume =       "125",
  number =       "1--3",
  pages =        "239--258",
  month =        mar,
  year =         "2000",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(99)00467-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Nov 14 11:21:52 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib",
  URL =          "http://cpc.cs.qub.ac.uk/summaries/ADLK;
                 http://www.elsevier.com/gej-ng//10/15/40/55/25/42/abstract.html",
  abstract =     "A study was conducted of multipliers for 128-bit
                 congruential pseudorandom number generators. Extensive
                 analysis and testing resulted in the identification of
                 over 2000 good multipliers of the form $ A = 5^k \bmod
                 2^{128} $, where $k$ is a prime number. The integer
                 lattice structure from any single multiplier is so fine
                 that it is not visible when {\tt REAL*8} values are
                 returned in up to four dimensions, or {\tt REAL*4}
                 values in seven dimensions. The multipliers are
                 designed to be used in sets, and are suitable for use
                 in massively-parallel computation.",
  acknowledgement = ack-nhfb,
  annote =       "This paper extends the authors' earlier work on 64-bit
                 generators \cite{Dyadkin:1997:FEL,Dyadkin:1997:SBM} to
                 128-bit arithmetic and more than 2000 generators, each
                 with a different multiplier.",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "Congruential; General purpose; Monte Carlo;
                 Multipliers; Pseudorandom; Random number generators;
                 Random numbers; Statistical methods",
}

@TechReport{Moler:2001:CCN,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: Normal Behavior: {Ziggurat}
                 algorithm generates normally distributed random
                 numbers",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  pages =        "1",
  month =        "Spring",
  year =         "2001",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.mathworks.com/company/newsletter/clevescorner/spring01_cleve.shtml",
  acknowledgement = ack-nhfb,
  annote =       "See \cite{Marsaglia:2000:ZMG} for the algorithm used
                 in Matlab's (version 5 and later) randn() function for
                 generating normally-distributed pseudo-random
                 numbers.",
  keywords =     "Matlab",
}

@Book{Robert:2004:MCS,
  author =       "Christian P. Robert and George Casella",
  title =        "{Monte Carlo} statistical methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xxx + 645",
  year =         "2004",
  ISBN =         "0-387-21239-6",
  ISBN-13 =      "978-0-387-21239-5",
  LCCN =         "QA276 .R575 2004",
  bibdate =      "Wed Jun 22 08:52:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Springer texts in statistics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/2004049157-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/2004049157-t.html;
                 http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-21239-5",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical statistics; Monte Carlo method; MCMCM
                 (Markov Chain Monte Carlo Methods)",
  tableofcontents = "Introduction \\
                 Random Variable Generation \\
                 Monte Carlo Integration \\
                 Controlling Monte Carlo Variance \\
                 Monte Carlo Optimization \\
                 Markov Chains \\
                 The Metropolis--Hastings Algorithm \\
                 The Slice Sampler \\
                 The Two-Stage Gibbs Sampler \\
                 The Multi-Stage Gibbs Sampler \\
                 Variable Dimension Models and Reversible Jump \\
                 Diagnosing Convergence \\
                 Perfect Sampling \\
                 Iterated and Sequential Importance Sampling",
}

@Article{Leong:2005:CIZ,
  author =       "Philip H. W. Leong and Ganglie Zhang and Dong-U",
  title =        "A Comment on the Implementation of the Ziggurat
                 Method",
  journal =      j-J-STAT-SOFT,
  volume =       "12",
  number =       "7",
  pages =        "1--44",
  month =        "????",
  year =         "2005",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Wed May 18 11:18:51 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "See \cite{Marsaglia:2000:ZMG}.",
  URL =          "http://www.jstatsoft.org/counter.php?id=114&url=v12/i07&ct=2;
                 http://www.jstatsoft.org/counter.php?id=114&url=v12/i07/v12i07.pdf&ct=1",
  abstract =     "We show that the short period of the uniform random
                 number generator in the published implementation of
                 Marsaglia and Tsang's Ziggurat method for generating
                 random deviates can lead to poor distributions.
                 Changing the uniform random number generator used in
                 its implementation fixes this issue.",
  accepted =     "2005-02-08",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  submitted =    "2005-02-08",
}

@Article{Panneton:2005:XRN,
  author =       "Fran{\c{c}}ois Panneton and Pierre L'Ecuyer",
  title =        "On the xorshift random number generators",
  journal =      j-TOMACS,
  volume =       "15",
  number =       "4",
  pages =        "346--361",
  month =        oct,
  year =         "2005",
  CODEN =        "ATMCEZ",
  DOI =          "https://doi.org/10.1145/1113316.1113319",
  ISSN =         "1049-3301 (print), 1558-1195 (electronic)",
  ISSN-L =       "1049-3301",
  bibdate =      "Thu Feb 16 10:42:56 MST 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tomacs/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  note =         "See
                 \cite{Marsaglia:2003:XR,Brent:2004:NMX,Vigna:2016:EEM}.",
  abstract =     "G. Marsaglia recently introduced a class of very fast
                 xorshift random number generators, whose implementation
                 uses three ``xorshift'' operations. They belong to a
                 large family of generators based on linear recurrences
                 modulo 2, which also includes shift-register
                 generators, the Mersenne twister, and several others.
                 In this article, we analyze the theoretical properties
                 of xorshift generators, search for the best ones with
                 respect to the equidistribution criterion, and test
                 them empirically. We find that the vast majority of
                 xorshift generators with only three xorshift
                 operations, including those having good
                 equidistribution, fail several simple statistical
                 tests. We also discuss generators with more than three
                 xorshifts.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Modeling and Computer Simulation",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J781",
}

@Article{Tu:2005:SRD,
  author =       "Shu-Ju Tu and Ephraim Fischbach",
  title =        "A Study on the Randomness of the Digits of $ \pi $",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "16",
  number =       "2",
  pages =        "281--294",
  month =        feb,
  year =         "2005",
  CODEN =        "IJMPEO",
  DOI =          "https://doi.org/10.1142/S0129183105007091",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  bibdate =      "Wed Jun 22 11:19:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "The statistical analysis in this work is flawed; see
                 \cite{Marsaglia:2005:RPO,Marsaglia:2006:RCS}",
  URL =          "http://www.worldscinet.com/ijmpc/16/1602/S01291831051602.html",
  abstract =     "We apply a newly-developed computational method,
                 Geometric Random Inner Products (GRIP), to quantify the
                 randomness of number sequences obtained from the
                 decimal digits of $ \pi $. Several members from the
                 GRIP family of tests are used, and the results from $
                 \pi $ are compared to those calculated from other
                 random number generators. These include a recent
                 hardware generator based on an actual physical process,
                 turbulent electroconvection. We find that the decimal
                 digits of $ \pi $ are in fact good candidates for
                 random number generators and can be used for practical
                 scientific and engineering computations.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
}

@Article{Agapie:2010:RPH,
  author =       "Stefan C. Agapie and Paula A. Whitlock",
  title =        "Random packing of hyperspheres and {Marsaglia}'s
                 parking lot test",
  journal =      j-MONTE-CARLO-METHODS-APPL,
  volume =       "16",
  number =       "3--4",
  pages =        "197--209",
  month =        dec,
  year =         "2010",
  CODEN =        "MCMAC6",
  DOI =          "https://doi.org/10.1515/mcma.2010.019",
  ISSN =         "0929-9629 (print), 1569-3961 (electronic)",
  ISSN-L =       "0929-9629",
  MRclass =      "65C05 (65C10)",
  MRnumber =     "2747812",
  bibdate =      "Wed Feb 29 09:27:54 MST 2012",
  bibsource =    "http://www.degruyter.com/view/j/mcma.2010.16.issue-3/issue-files/mcma.2010.16.issue-3.xml;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/mcma.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.degruyter.com/view/j/mcma.2010.16.issue-3-4/mcma.2010.019/mcma.2010.019.xml",
  acknowledgement = ack-nhfb,
  fjournal =     "Monte Carlo Methods and Applications",
  journal-URL =  "http://www.degruyter.com/view/j/mcma",
  keywords =     "CDC 48-bit multiplicative congruential generator {\tt
                 rannyu()}",
  remark =       "The authors investigate the connection between the
                 hypersphere packing problem and Marsaglia's parking lot
                 test \cite{Marsaglia:1985:CVR} for correlations in
                 random number generator output.",
}

@Article{Anonymous:2011:OGM,
  author =       "Anonymous",
  title =        "Obituary: {George Marsaglia (1924--2011)}",
  journal =      "{Tallahassee Democrat}",
  pages =        "??--??",
  day =          "22",
  month =        feb,
  year =         "2011",
  ISSN =         "0738-5153",
  bibdate =      "Mon Jan 07 18:23:00 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://www.legacy.com/obituaries/tallahassee/obituary.aspx?n=george-marsaglia",
  acknowledgement = ack-nhfb,
}

@TechReport{Rose:2011:KBT,
  author =       "Greg Rose",
  title =        "{KISS}: {A} Bit Too Simple",
  type =         "Report",
  number =       "??",
  institution =  "Qualcomm Inc.",
  address =      "????",
  day =          "18",
  month =        apr,
  year =         "2011",
  bibdate =      "Wed Jun 22 08:40:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  URL =          "http://eprint.iacr.org/2011/007.pdf",
  abstract =     "KISS (`Keep it Simple Stupid') is an efficient
                 pseudo-random number generator originally specified by
                 G. Marsaglia and A. Zaman in 1993. G. Marsaglia in 1998
                 posted a C version to various USENET newsgroups,
                 including sci.crypt. Marsaglia himself has never
                 claimed cryptographic security for the KISS generator,
                 but others have made the intellectual leap and claimed
                 that it is of cryptographic quality. In this paper we
                 show a number of reasons why the generator does not
                 meet some of the KISS authors' claims, why it is not
                 suitable for use as a stream cipher, and that it is not
                 cryptographically secure. Our best attack requires
                 about 70 words of generated output and a few hours of
                 computation to recover the initial state. In early
                 2011, G. Marsaglia posted a new version of KISS, which
                 falls to a simple divide-and-conquer attack.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Salmon:2011:PRN,
  author =       "John K. Salmon and Mark A. Moraes and Ron O. Dror and
                 David E. Shaw",
  title =        "Parallel random numbers: as easy as $ 1, 2, 3 $",
  crossref =     "Lathrop:2011:SPI",
  pages =        "16:1--16:12",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/2063384.2063405",
  bibdate =      "Fri Dec 16 11:05:47 MST 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  abstract =     "Most pseudorandom number generators (PRNGs) scale
                 poorly to massively parallel high-performance
                 computation because they are designed as sequentially
                 dependent state transformations. We demonstrate that
                 independent, keyed transformations of counters produce
                 a large alternative class of PRNGs with excellent
                 statistical properties (long period, no discernable
                 structure or correlation). These counter-based PRNGs
                 are ideally suited to modern multicore CPUs, GPUs,
                 clusters, and special-purpose hardware because they
                 vectorize and parallelize well, and require little or
                 no memory for state. We introduce several counter-based
                 PRNGs: some based on cryptographic standards (AES,
                 Threefish) and some completely new (Philox). All our
                 PRNGs pass rigorous statistical tests (including
                 TestU01's BigCrush) and produce at least 264 unique
                 parallel streams of random numbers, each with period
                 2128 or more. In addition to essentially unlimited
                 parallel scalability, our PRNGs offer excellent
                 single-chip performance: Philox is faster than the
                 CURAND library on a single NVIDIA GPU.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  remark-1 =     "From the article, page 3: ``The period of any useful
                 PRNG must be sufficiently long that the state space of
                 the PRNG will not be exhausted by any application, even
                 if run on large parallel machines for long periods of
                 time. One million cores, generating 10 billion random
                 numbers per second, will take about half an hour to
                 generate $2^{64}$ random numbers, which raises doubts
                 about the long-term viability of a single,
                 unpararameterized PRNG with a periods of `only'
                 $2^{64}$. On the other hand, exhausting the state space
                 of a multistreamable family of $2^{32}$ such
                 generators, or a single generator with a period of
                 $2^{128}$, is far beyond the capability of any
                 technology remotely like that in current computers.''",
  remark-2 =     "From the article, page 5: ``only a few conventional
                 PRNGs pass even one complete battery of Crush tests.
                 The multiple recursive generators, the multiplicative
                 lagged Fibonacci generators, and some combination
                 generators are reported to do so. On the other hand,
                 many of the most widely used PRNGs fail quite
                 dramatically, including all of the linear congruential
                 generators, such as drand48() and the C-language
                 rand(). The linear and general feedback shift register
                 generators, including the Mersenne Twister, always fail
                 the tests of linear dependence, and some fail many
                 more.''",
  remark-3 =     "This article has a good discussion of the issues of
                 parallel random-number generation. The authors note
                 that large internal state (e.g., the Mersenne Twister
                 needs 2496 bytes) is impractical with a million cores,
                 or with GPUs that require awkward memory transfers
                 between GPU and CPU memory. They propose methods that
                 require little state, and are based on cryptographic
                 algorithms. They point out that a generator based on
                 the Advanced Encryption Standard with Intel AES-NI
                 hardware support becomes competitive with other
                 generators. The comparative Table 2 on page 8 shows
                 that the Threefish, Threefry, and Philox generators
                 require only 0.7 to 4.3 cycles per byte.",
}

@Misc{Saito:2012:DCS,
  author =       "Mutsuo Saito and Makoto Matsumoto",
  title =        "A deviation of {CURAND}: Standard pseudorandom number
                 generator in {CUDA} for {GPGPU}",
  howpublished = "Slides presented at the Tenth International Conference
                 on Monte Carlo and Quasi-Monte Carlo Methods in
                 Scientific Computing",
  month =        feb,
  year =         "2012",
  bibdate =      "Wed May 13 11:21:03 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  URL =          "http://www.mcqmc2012.unsw.edu.au/slides/MCQMC2012_Matsumoto.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The slides report that Marsaglia's {\tt xorwow()}
                 long-period ($ (2^{160} - 1) 2^{32}$) generator
                 \cite{Marsaglia:2003:XR} is rejected by three of the
                 BigCrush tests (Collision Over, Simplified Poker Test,
                 and Linear Complexity Test) in the TESTU01 suite, and
                 the authors conclude: ``{\tt xorwow} is not suitable
                 for serious Monte Carlo''.",
}

@Article{Steele:2014:FSP,
  author =       "Guy L. {Steele, Jr.} and Doug Lea and Christine H.
                 Flood",
  title =        "Fast splittable pseudorandom number generators",
  journal =      j-SIGPLAN,
  volume =       "49",
  number =       "10",
  pages =        "453--472",
  month =        oct,
  year =         "2014",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2714064.2660195",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue May 12 17:41:21 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib",
  abstract =     "We describe a new algorithm SplitMix for an
                 object-oriented and splittable pseudorandom number
                 generator (PRNG) that is quite fast: 9 64-bit
                 arithmetic/logical operations per 64 bits generated. A
                 conventional linear PRNG object provides a generate
                 method that returns one pseudorandom value and updates
                 the state of the PRNG, but a splittable PRNG object
                 also has a second operation, split, that replaces the
                 original PRNG object with two (seemingly) independent
                 PRNG objects, by creating and returning a new such
                 object and updating the state of the original object.
                 Splittable PRNG objects make it easy to organize the
                 use of pseudorandom numbers in multithreaded programs
                 structured using fork-join parallelism. No locking or
                 synchronization is required (other than the usual
                 memory fence immediately after object creation).
                 Because the generate method has no loops or
                 conditionals, it is suitable for SIMD or GPU
                 implementation. We derive SplitMix from the DotMix
                 algorithm of Leiserson, Schardl, and Sukha by making a
                 series of program transformations and engineering
                 improvements. The end result is an object-oriented
                 version of the purely functional API used in the
                 Haskell library for over a decade, but SplitMix is
                 faster and produces pseudorandom sequences of higher
                 quality; it is also far superior in quality and speed
                 to java.util.Random, and has been included in Java JDK8
                 as the class java.util.SplittableRandom. We have tested
                 the pseudorandom sequences produced by SplitMix using
                 two standard statistical test suites (DieHarder and
                 TestU01) and they appear to be adequate for
                 ``everyday'' use, such as in Monte Carlo algorithms and
                 randomized data structures where speed is important.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark-1 =     "OOPSLA '14 conference proceedings.",
  remark-2 =     "On page 466, the authors describe an interesting
                 technique for improving a user-supplied seed that might
                 produce insufficient randomness in the next several
                 members of the random-number sequence: ``Long runs of
                 0-bits or of 1-bits in the $\gamma$ [candidate seed]
                 value do not cause bits of the seed to flip; an
                 approximate proxy for how many bits of the seed will
                 flip might be the number of bit pairs of the form 01 or
                 10 in the candidate $\gamma$ value {\tt z}. Therefore
                 we require that the number of such pairs, as computed
                 by {\tt Long.bitCount(z ^ (z >>> 1))}, exceed 24; if it
                 does not, then the candidate z is replaced by the XOR
                 of {\tt z} and {\tt 0xaaaaaaaaaaaaaaaaL}, a constant
                 chosen so that (a) the low bit of {\tt z} remains 1,
                 and (b) every bit pair of the form 00 or 11 becomes
                 either 01 or 10, and likewise every bit pair of the
                 form 01 or 10 becomes either 00 or 11, so the new value
                 necessarily has more than 24 bit pairs whose bits
                 differ. Testing shows that this trick appears to be
                 effective.''",
  remark-3 =     "From page 468: ``we did three runs of TestU01 BigCrush
                 on {\tt java.util.Random}; 19 tests produced clear
                 failure on all three runs. These included 9 Birthday
                 Spacings tests, 8 ClosePairs tests, a WeightDistrib
                 test, and a CouponCollector test. This confirms
                 L'Ecuyer's observation that {\tt java.util.Random}
                 tends to fail Birthday Spacings tests [17].'' The
                 reference is to \cite{LEcuyer:2001:SUR}.",
  remark-4 =     "From page 470: ``[L'Ecuyer] comments, `In the Java
                 class {\tt java.util.Random}, RNG streams can be
                 declared and constructed dynamically, without limit on
                 their number. However, no precaution seems to have been
                 taken regarding the independence of these streams.'''",
  remark-5 =     "From page 471: ``They [the generators in this paper]
                 should not be used for cryptographic or security
                 applications, because they are too predictable (the
                 mixing functions are easily inverted, and two
                 successive outputs suffice to reconstruct the internal
                 state), \ldots{} One version seems especially suitable
                 for use as a replacement for {\tt java.util.Random},
                 because it produces sequences of higher quality, is
                 faster in sequential use, is easily parallelized for
                 use in JDK8 stream expressions, and is amenable to
                 efficient implementation on SIMD and GPU
                 architectures.''",
}

@Article{Vigna:2016:EEM,
  author =       "Sebastiano Vigna",
  title =        "An Experimental Exploration of {Marsaglia}'s {\tt
                 xorshift} Generators, Scrambled",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "30:1--30:23",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2845077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2845077",
  abstract =     "Marsaglia proposed xorshift generators are a class of
                 very fast, good-quality pseudorandom number generators.
                 Subsequent analysis by Panneton and L'Ecuyer has
                 lowered the expectations raised by Marsaglia's article,
                 showing several weaknesses of such generators.
                 Nonetheless, many of the weaknesses of xorshift
                 generators fade away if their result is scrambled by a
                 nonlinear operation (as originally suggested by
                 Marsaglia). In this article we explore the space of
                 possible generators obtained by multiplying the result
                 of a xorshift generator by a suitable constant. We
                 sample generators at 100 points of their state space
                 and obtain detailed statistics that lead us to choices
                 of parameters that improve on the current ones. We then
                 explore for the first time the space of
                 high-dimensional xorshift generators, following another
                 suggestion in Marsaglia's article, finding choices of
                 parameters providing periods of length $ 2^{1024} 1 $
                 and $ 2^{4096} 1 $. The resulting generators are of
                 extremely high quality, faster than current similar
                 alternatives, and generate long-period sequences
                 passing strong statistical tests using only eight
                 logical operations, one addition, and one
                 multiplication by a constant.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
}

%%% ====================================================================
%%% These entries must come last because they are cross-referenced
%%% by others above.

@Proceedings{Kozesnik:1964:TTP,
  editor =       "Jaroslav Ko{\v{z}}e{\v{s}}n{\'\i}k",
  booktitle =    "{Transactions of the third Prague conference on
                 information theory, statistical decision functions,
                 random processes held at Liblice near Prague, from June
                 5 to 13, 1962}",
  title =        "{Transactions of the third Prague conference on
                 information theory, statistical decision functions,
                 random processes held at Liblice near Prague, from June
                 5 to 13, 1962}",
  publisher =    "Czechoslovak Academy of Science",
  address =      "Prague, Czechoslovakia",
  pages =        "846",
  year =         "1964",
  LCCN =         "????",
  bibdate =      "Thu Aug 05 05:58:29 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  note =         "In memory of RNDr. Antonin Spacek.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kozesnik:1967:TFP,
  editor =       "Jaroslav Ko{\v{z}}e{\v{s}}n{\'\i}k",
  booktitle =    "{Transactions of the fourth Prague conference on
                 information theory, statistical decision functions,
                 random processes, held at Prague, from August 31 to
                 September 11, 1965}",
  title =        "{Transactions of the fourth Prague conference on
                 information theory, statistical decision functions,
                 random processes, held at Prague, from August 31 to
                 September 11, 1965}",
  publisher =    "Academia",
  address =      "Prague, Czechoslovakia",
  pages =        "725",
  year =         "1967",
  LCCN =         "????",
  bibdate =      "Thu Aug 05 06:05:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Talbot:1969:ATP,
  editor =       "A. (Alan) Talbot",
  booktitle =    "{Approximation theory: proceedings of a symposium held
                 at Lancaster, July 1969}",
  title =        "{Approximation theory: proceedings of a symposium held
                 at Lancaster, July 1969}",
  publisher =    "Academic Press",
  address =      "London",
  pages =        "viii + 356",
  year =         "1969",
  ISBN =         "0-12-682250-6",
  ISBN-13 =      "978-0-12-682250-2",
  LCCN =         "QA221 .A66",
  bibdate =      "Thu Aug 05 06:10:49 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  remark =       "Papers from a conference held at the Mathematics
                 Department, University of Lancaster 21--25 July 1969.",
}

@Proceedings{Zaremba:1972:ANT,
  editor =       "S. K. Zaremba",
  booktitle =    "{Applications of Number Theory to Numerical Analysis =
                 Applications de la th{\'e}orie des nombres {\`a}
                 l'analyse num{\'e}rique. Proceedings of the symposium
                 at the Centre for Research in Mathematics, University
                 of Montreal, September 9--14, 1971}",
  title =        "{Applications of Number Theory to Numerical Analysis =
                 Applications de la th{\'e}orie des nombres {\`a}
                 l'analyse num{\'e}rique. Proceedings of the symposium
                 at the Centre for Research in Mathematics, University
                 of Montreal, September 9--14, 1971}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 489",
  year =         "1972",
  ISBN =         "0-12-775950-6",
  ISBN-13 =      "978-0-12-775950-0",
  LCCN =         "QA297 .A67",
  bibdate =      "Mon Aug 02 10:53:03 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
  language =     "French and English",
}

@Proceedings{Saleh:1975:PSS,
  editor =       "A. K. Md. Ehsanes Saleh",
  booktitle =    "{Proceedings of the Symposium on Statistics and
                 Related Topics: October 24--26, 1974, Carleton
                 University, Ottawa}",
  title =        "{Proceedings of the Symposium on Statistics and
                 Related Topics: October 24--26, 1974, Carleton
                 University, Ottawa}",
  volume =       "12",
  publisher =    "Carleton University",
  address =      "Ottawa, ON, Canada",
  pages =        "437",
  year =         "1975",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0318-6288",
  LCCN =         "QA276.A1 S92 1974",
  bibdate =      "Thu Aug 05 06:14:23 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  series =       "Carleton mathematical lecture notes",
  acknowledgement = ack-nhfb,
}

@Book{Ralston:1976:ECS,
  editor =       "Anthony Ralston and Chester L. Meek",
  booktitle =    "Encyclopedia of computer science",
  title =        "Encyclopedia of computer science",
  publisher =    "Petrocelli\slash Charter",
  address =      "New York, NY, USA",
  pages =        "xxviii + 1523",
  year =         "1976",
  ISBN =         "0-88405-321-0",
  ISBN-13 =      "978-0-88405-321-7",
  LCCN =         "QA76.15 .E55 1976",
  bibdate =      "Mon Aug 02 16:32:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Book{Ralston:1983:ECS,
  editor =       "Anthony Ralston and Edwin D. {Reilly, Jr.}",
  booktitle =    "Encyclopedia of Computer Science and Engineering",
  title =        "Encyclopedia of Computer Science and Engineering",
  publisher =    pub-VAN-NOSTRAND-REINHOLD,
  address =      pub-VAN-NOSTRAND-REINHOLD:adr,
  edition =      "Second",
  pages =        "xxix + 1664",
  year =         "1983",
  ISBN =         "0-442-24496-7",
  ISBN-13 =      "978-0-442-24496-5",
  LCCN =         "QA76.15 .E48 1983",
  bibdate =      "Mon Aug 02 10:58:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Billard:1985:CSS,
  editor =       "L. (Lynne) Billard",
  booktitle =    "{Computer science and statistics: proceedings of the
                 Sixteenth Symposium on the Interface, Atlanta, Georgia,
                 March 1984}",
  title =        "{Computer science and statistics: proceedings of the
                 Sixteenth Symposium on the Interface, Atlanta, Georgia,
                 March 1984}",
  publisher =    pub-ELS,
  address =      pub-ELS:adr,
  pages =        "xi + 296",
  year =         "1985",
  ISBN =         "0-444-87725-8",
  ISBN-13 =      "978-0-444-87725-3",
  LCCN =         "QA276.4 .S95 1984",
  bibdate =      "Thu Dec 18 13:41:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Wegman:1988:CSS,
  editor =       "Edward J. Wegman and Donald T. Gantz and John J.
                 Miller",
  title =        "{Computing Science and Statistics Proceedings of the
                 20th Symposium on the Interface Fairfax, Virginia,
                 April 1988}",
  publisher =    "American Statistical Association",
  address =      "Alexandria, VA, USA",
  pages =        "xxxvii + 860",
  year =         "1988",
  bibdate =      "Wed Nov 12 16:41:33 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a208838.pdf",
  acknowledgement = ack-nhfb,
}

@Proceedings{Wegman:1988:SIC,
  editor =       "Edward J. Wegman",
  booktitle =    "{20th Symposium on the Interface: Computing Science
                 and Statistics: Theme: Computationally Intensive
                 Methods in Statistics April 20--23, 1988}",
  title =        "{20th Symposium on the Interface: Computing Science
                 and Statistics: Theme: Computationally Intensive
                 Methods in Statistics April 20--23, 1988}",
  publisher =    "Interface Foundation of North America, Inc.",
  address =      "P.O. Box 7460, Fairfax Station, VA 22039-7460, USA",
  pages =        "iv + 185",
  year =         "1988",
  bibdate =      "Wed Nov 12 16:36:54 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a205068.pdf",
  acknowledgement = ack-nhfb,
}

@Proceedings{Gleser:1989:CPS,
  editor =       "Leon Jay Gleser and others",
  booktitle =    "Contributions to probability and statistics: essays in
                 honor of {Ingram Olkin}",
  title =        "Contributions to probability and statistics: essays in
                 honor of {Ingram Olkin}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 505",
  year =         "1989",
  ISBN =         "0-387-97076-2, 3-540-97076-2",
  ISBN-13 =      "978-0-387-97076-9, 978-3-540-97076-7",
  LCCN =         "QA273.18 .C683 1989",
  bibdate =      "Thu Aug 05 06:19:18 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Burr:1992:UEN,
  editor =       "Stefan A. Burr",
  booktitle =    "{The unreasonable effectiveness of number theory:
                 American Mathematical Society short course, August
                 6--7, 1991, Orono, Maine}",
  title =        "{The unreasonable effectiveness of number theory:
                 American Mathematical Society short course, August
                 6--7, 1991, Orono, Maine}",
  volume =       "46",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 156",
  year =         "1992",
  ISBN =         "0-8218-5501-8",
  ISBN-13 =      "978-0-8218-5501-0",
  LCCN =         "QA241 .U67 1992",
  bibdate =      "Thu Aug 05 06:26:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib",
  series =       "Proceedings of symposia in applied mathematics",
  acknowledgement = ack-nhfb,
  tableofcontents = "The unreasonable effectiveness of number theory in
                 physics, communication and music / Manfred R. Schroeder
                 [1--20] \\
                 The reasonable and unreasonable effectiveness of number
                 theory in statistical mechanics / George E. Andrews
                 [21--34]\\
                 Number theory and dynamical systems / J.C. Lagarias
                 [35--72] \\
                 The mathematics of random number generators / George
                 Marsaglia [73--90] \\
                 Cyclotomy and cyclic codes / Vera Pless [91--104] \\
                 Number theory in computer graphics / M. Douglas McIlroy
                 [105--122]",
}

@Article{Grassberger:1993:CGR,
  author =       "Peter Grassberger",
  title =        "On correlations in ``good'' random number generators",
  journal =      j-PHYS-LET-A,
  volume =       "181",
  number =       "1",
  pages =        "43--46",
  day =          "27",
  month =        sep,
  year =         "1993",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/0375-9601(93)91122-L",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Wed Feb 22 09:13:21 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "See \cite{Ferrenberg:1992:MCS}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/037596019391122L",
  abstract =     "By studying a different system, we verify the
                 correlations found recently in a popular random number
                 generator by Ferrenberg et al. We find indeed that the
                 dominant correlations are too long ranged to be seen by
                 them, and we check a number of further RNGs.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  remark-corr =  "See \cite{Kalle:1984:PRN, Berdnicov:1991:MCS,
                 Ferrenberg:1992:MCS, Grassberger:1993:CGR,
                 Kankaala:1993:BLC, Selke:1993:CFM, Coddington:1994:ARN,
                 Holian:1994:PNG, Vattulainen:1994:PTR,
                 Compagner:1995:OCR, Schmid:1995:EMC,
                 Vattulainen:1995:CSS, Vattulainen:1995:PMT,
                 Bromley:1996:QNG, Coddington:1997:RNG, Shchur:1997:CMC,
                 Shchur:1997:SDR, DSouza:1998:SBD, Gammel:1998:HRR,
                 Resende:1998:URN, Mertens:2003:EPR, Bauke:2004:PRC,
                 Mertens:2004:EPR, Ossola:2004:SED} for examples of
                 generator correlations causing Monte Carlo simulations
                 in physics to converge to the wrong answer.",
}

@Book{Ralston:1993:ECS,
  editor =       "Anthony Ralston and Edwin D. {Reilly, Jr.}",
  booktitle =    "Encyclopedia of Computer Science and Engineering",
  title =        "Encyclopedia of Computer Science and Engineering",
  publisher =    pub-VAN-NOSTRAND-REINHOLD,
  address =      pub-VAN-NOSTRAND-REINHOLD:adr,
  edition =      "Third",
  pages =        "xxv + 1558",
  year =         "1993",
  ISBN =         "0-442-27679-6",
  ISBN-13 =      "978-0-442-27679-9",
  LCCN =         "QA76.15 .E48 1993",
  bibdate =      "Mon Aug 02 10:58:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib",
  acknowledgement = ack-nhfb,
}

@Book{Ralston:2003:ECS,
  editor =       "Anthony Ralston and Edwin D. Reilly and David
                 Hemmendinger",
  booktitle =    "Encyclopedia of Computer Science",
  title =        "Encyclopedia of Computer Science",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Fourth",
  bookpages =    "xxix + 2034",
  pages =        "xxix + 2034",
  year =         "2003",
  ISBN =         "0-470-86412-5",
  ISBN-13 =      "978-0-470-86412-8",
  LCCN =         "QA76.15 .E48 2003",
  bibdate =      "Wed Jun 22 06:58:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.e-streams.com/es0707/es0707\_3357.htm;
                 http://www.loc.gov/catdir/bios/wiley046/2003283283.htm;
                 http://www.loc.gov/catdir/description/wiley041/2003283283.htm;
                 http://www.loc.gov/catdir/toc/wiley041/2003283283.htm",
  acknowledgement = ack-nhfb,
  remark =       "Previously published: London : Nature Publishing
                 Group, 2000.",
  subject =      "Computer science; Encyclopedias; Information science",
}

@Proceedings{Lathrop:2011:SPI,
  editor =       "Scott Lathrop and Jim Costa and William Kramer",
  booktitle =    "{SC'11: Proceedings of 2011 International Conference
                 for High Performance Computing, Networking, Storage and
                 Analysis, Seattle, WA, November 12--18 2011}",
  title =        "{SC'11: Proceedings of 2011 International Conference
                 for High Performance Computing, Networking, Storage and
                 Analysis, Seattle, WA, November 12--18 2011}",
  publisher =    pub-ACM # " and " # pub-IEEE,
  address =      pub-ACM:adr # " and " # pub-IEEE:adr,
  bookpages =    "866",
  pages =        "866",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/2063384",
  ISBN =         "1-4503-0771-X",
  ISBN-13 =      "978-1-4503-0771-0",
  LCCN =         "QA76.5 .S96 2011",
  bibdate =      "Fri Dec 16 11:11:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
  acknowledgement = ack-nhfb,
  xxeditor =     "{ACM}",
}

.