International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Uniform Random Number Generators

  • Pierre L’Ecuyer
Reference work entry


A growing number of modern statistical tools are based on Monte Carlo ideas; they sample independent random variables by computer to estimate distributions, averages, quantiles, roots or optima of functions, etc. These methods are developed and studied in the abstract framework of probability theory, in which the notion of an infinite sequence of independent random variables uniformly distributed over the interval (0, 1) (i.i.d. \(\mathcal{U}(0,1)\)

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References and Further Reading

  1. Asmussen S, Glynn PW (2007) Stochastic simulation. Springer-Verlag, New YorkzbMATHGoogle Scholar
  2. Chor B, Goldreich O (1988) Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J Comput 17(2):230–261CrossRefzbMATHMathSciNetGoogle Scholar
  3. Glasserman P (2004) Monte Carlo methods in financial engineering. Springer-Verlag, New YorkzbMATHGoogle Scholar
  4. Knuth DE (1998) The art of computer programming, vol 2: seminumerical algorithms, 3rd edn. Addison-Wesley, Reading, MAGoogle Scholar
  5. Law AM, Kelton WD (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  6. L’Ecuyer P (1996) Combined multiple recursive random number generators. Oper Res 44(5):816–822CrossRefzbMATHGoogle Scholar
  7. L’Ecuyer P (1997) Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J Comput 9(1):57–60CrossRefzbMATHMathSciNetGoogle Scholar
  8. L’Ecuyer P (1999a) Good parameters and implementations for combined multiple recursive random number generators. Oper Res 47(1):159–164CrossRefzbMATHMathSciNetGoogle Scholar
  9. L’Ecuyer P (1999b) Tables of maximally equidistributed combined LFSR generators. Math Comput 68(225):261–269CrossRefzbMATHMathSciNetGoogle Scholar
  10. L’Ecuyer P (2004)  Chapter II.2: Random number generation. In: Gentle JE, Haerdle W, Mori Y (eds) Handbook of computational statistics, Springer-Verlag, Berlin, pp 35–70Google Scholar
  11. L’Ecuyer P (2006)  Chapter 3: Uniform random number generation. In: Henderson SG, Nelson BL (eds) Simulation, Handbooks in operations research and management science, Elsevier, Amsterdam, pp 55–81CrossRefGoogle Scholar
  12. L’Ecuyer P (2008) SSJ: A Java library for stochastic simulation, software user’s guide. Available at ∼ lecuyer.
  13. L’Ecuyer P, Granger-Piché J (2003) Combined generators with components from different families. Math Comput Simul 62: 395–404CrossRefzbMATHGoogle Scholar
  14. L’Ecuyer P, Panneton F (2009) F2-linear random number generators. In: Alexopoulos C, Goldsman D, Wilson JR (eds) Advancing the frontiers of simulation: a festschrift in honor of George Samuel Fishman. Springer-Verlag, New York, pp 169–193CrossRefGoogle Scholar
  15. L’Ecuyer P, Simard R (2007) TestU01: a C library for empirical testing of random number generators. ACM Trans Math Softw 33(4):22CrossRefMathSciNetGoogle Scholar
  16. L’Ecuyer P, Simard R, Chen EJ, Kelton WD (2002) An object-oriented random-number package with many long streams and substreams. Oper Res 50(6):1073–1075CrossRefGoogle Scholar
  17. L’Ecuyer P, Touzin R (2000) Fast combined multiple recursive generators with multipliers of the form a = ± 2q ± 2r. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 2000 winter simulation conference. IEEE Press, Piscataway, NJ, pp 683–689CrossRefGoogle Scholar
  18. Marsaglia G (1996) DIEHARD: a battery of tests of randomness. Accessed 3 Aug 2010
  19. Matsumoto M, Nishimura T (1998) Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8(1):3–30CrossRefzbMATHGoogle Scholar
  20. Panneton F, L’Ecuyer P, Matsumoto M (2006) Improved long-period generators based on linear recurrences modulo 2. ACM Trans Math Softw 32(1):1–16CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pierre L’Ecuyer
    • 1
  1. 1.Université de MontréalMontréal, QCCanada