This section lists some of the source reference material used in programming the random generators and distributions. The following is a list of source articles or books from which the generator and distribution objects were implemented
LCG. a golden oldie; see [Knuth 1981] or [Numerical Recipes].
PMMLCG. see [Park & Miller 1988], [L'Ecuyer & Cote 1991] and [L'Ecuyer & Andres 1997].
ACG. a golden oldie; see [Knuth 1981] or [Numerical Recipes].
SCG. a golden oldie; see [Knuth 1981] or [Numerical Recipes].
SWB. see [Marsaglia & Zaman 1991]
PSWB. see [Marsaglia & Zaman 1991]
MRG. see [L'Ecuyer et al 1993]
C2MRG3. see [L'Ecuyer 1996(a)] and [L'Ecuyer 1999(a)]
C2TAUS. see [Tezuka & L'Ecuyer 1991], [L'Ecuyer 1996(b)] and [L'Ecuyer 1999(b)]. Also [Tausworthe 1965].
TGFSR (TT800, TT775, TT403). see [Matsumoto & Kurita 1992] and [Matsumoto & Kurita 1994].
MT19937. see [Matsumoto & Nishimura 1998].
MWCA, MWCB, C3MWC, RWC2, RWC8 ("Mother"). See [Marsaglia 1994(a)] and [Marsaglia 1994(b)].
C2LCGX. See [L'Ecuyer & Cote 1991]
C4LCGX. See [L'Ecuyer & Andres 1997]
RandomBitDist. Code contributed by Nelson Minar.
BernoulliDist. Code contributed by Barry McMullin.
UniformIntegerDist. Code contributed by Nelson Minar.
UniformUnsignedDist. Code contributed by Nelson Minar.
UniformDoubleDist. Code contributed by Nelson Minar.
NormalDist. See [Numerical Recipes].
LogNormalDist. See [Numerical Recipes].
ExponentialDist. See [Russell 1992].
GammaDist. See [Watkins 1994].
Pierre L'Ecuyer maintains a personal web site . He has many of his own papers there, as well as further links. He has papers both on generating random numbers and on testing random number generators.
George Marsaglia has a personal web site. His battery of tests for random generators, called Diehard, is not available there, but rather from Hong Kong. A GUI version of Diehard has been under development for some time, but is not yet ready.
The pLab project in Salzburg, Austria, also has much useful information.
[Ferrenberg et al 1992] | Alan M. Ferrenberg, D. P. Landau, and Y. Joanna Wong, "Monte Carlo Simulations: Hidden Errors from "Good" Random Number Generators": Physical Review Letters, no. 23, vol. 69, December, 1992. |
[Knuth 1981] | Donald Knuth, The Art of Computer Programming, 2nd ed., vol. II, Seminumerical Algorithms, Addison-Wesley, Reading, 1981. |
[L'Ecuyer et al 1993] | Pierre L'Ecuyer, F. Blouin, and R. Couture, "A Search for Good Multiple Recursive Random Generators.": ACM TOMACS, vol. 3, pp. 87-98, 1993. |
[L'Ecuyer 1996(a)] | Pierre L'Ecuyer, "Combined Multiple Recursive Generators.": Operations Research, no. 5, vol. 44, pp. 816-822, 1997. |
[L'Ecuyer 1996(b)] | Pierre L'Ecuyer, "Maximally Equidistributed Combined Tausworthe Generators": Mathematics and Computation, no. 65, vol. 213, pp. 203-213, 1996. |
[L'Ecuyer 1999(a)] | Pierre L'Ecuyer, "Good Parameter Sets for Combined Multiple Recursive Random Number Generators": Operations Research, no. 1, vol. 47, pp. 159-164, 1999. |
[L'Ecuyer 1999(b)] | Pierre L'Ecuyer, "Tables of Maximally-Equidistributed Combined LFSR Generators": Mathematics and Computation, no. 225, vol. 68, pp. 261-269, 1999. |
[L'Ecuyer & Andres 1997] | Pierre L'Ecuyer and Terry H. Andres, "A Random Number Generator Based on the Combination of Four LCGs.": Mathematics and Computers in Simulation, vol. 44, pp. 99-107, 1997. |
[L'Ecuyer & Cote 1991] | Pierre L'Ecuyer and Serge Cote, "Implementing a Random Number Package with Splitting Facilities": ACM TOMACS, no. 1, vol. 17, pp. 98-111, March, 1991. |
[Marsaglia 1994(a)] | George Marsaglia, "The Mother of All Random Generators": Posted by Bob Wheeler to sci.stat.consult and sci.math.num-analysis on behalf of George Marsaglia on October 28, 1994. The code is available at ftp.taygeta.com . |
[Marsaglia 1994(b)] | George Marsaglia, "Multiply-With-Carry Generators": File "mwc1.ps" on Marsaglia's Diehard CD-ROM, available online at ftp.csis.hku.hk. |
[Marsaglia & Zaman 1991] | George Marsaglia and Arif Zaman, "A New Class of Random Number Generators.": Annals of Applied Probability, no. 3, vol. 3, pp. 462-480. |
[Matsumoto & Kurita 1992] | M. Matsumoto and Y. Kurita, "Twisted GFSR generators": ACM TOMACS, vol. 2, 1992, pp. 179-194. |
[Matsumoto & Kurita 1994] | Makoto Matsumoto and Yoshiharu Kurita, "Twisted GFSR Generators II": ACM TOMACS (Amended by K. Matsumoto, 8 July 1996)., no. 3, vol. 4, pp. 254-266. |
[Matsumoto & Nishimura 1998] | M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudorandomnumber Generator": ACM TOMACS, no. 1, vol. 8, pp. 3-30, 17 December 1998. |
[Nature 1994] | "News and Views": Nature, vol. 372, December, 1994. |
[Numerical Recipes] | W. H. Press, S. A Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed., Cambridge University Press, 1992. |
[Park & Miller 1988] | Stephen K. Park and Keith W. Miller, "Random Number Generators: Good Ones Are Hard to Find.": CACM, no. 10, vol. 31, pp. 1192-1201, October 1988. |
[Tausworthe 1965] | R.C. Tausworthe, "Random Numbers Generated by Linear Recurrence modulo 2": Math. Comput., vol. 19, pp. 201-209, 1965. |
[Tezuka & L'Ecuyer 1991] | Shu Tezuka and Pierre L'Ecuyer, "Efficient and Portable Combined Tausworthe Random Number Generators.": ACM TOMACS, no. 2, vol. 1, pp. 99-112. |
[Russell 1992] | Edward C. Russell, "Building Simulation Models With SIMSCRIPT II.5", CACI Products Company, La Jolla, 1992, The company's web site is: http://www.caciasl.com. |
[Watkins 1994] | Kevin Watkins, Discrete Event Simulation in C, McGraw-Hill, 1994. |