Introduction
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. \(\mathcal{U}(0,1)\)), for example, is well-defined, and the theory is built under the assumption that such random variables can be sampled at will. But in reality, the notion of i.i.d. random variables cannot be implemented exactly on current computers. It can be approximated to some extent by physical devices, but these approximations are cumbersome, inconvenient, and not always reliable, so they are rarely used for computational statistics. Random number generators used for Monte Carlo applications are in reality deterministic algorithms whose...
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References and Further Reading
Asmussen S, Glynn PW (2007) Stochastic simulation. Springer-Verlag, New York
Chor B, Goldreich O (1988) Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J Comput 17(2):230–261
Glasserman P (2004) Monte Carlo methods in financial engineering. Springer-Verlag, New York
Knuth DE (1998) The art of computer programming, vol 2: seminumerical algorithms, 3rd edn. Addison-Wesley, Reading, MA
Law AM, Kelton WD (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New York
L’Ecuyer P (1996) Combined multiple recursive random number generators. Oper Res 44(5):816–822
L’Ecuyer P (1997) Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J Comput 9(1):57–60
L’Ecuyer P (1999a) Good parameters and implementations for combined multiple recursive random number generators. Oper Res 47(1):159–164
L’Ecuyer P (1999b) Tables of maximally equidistributed combined LFSR generators. Math Comput 68(225):261–269
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 35–70
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 55–81
L’Ecuyer P (2008) SSJ: A Java library for stochastic simulation, software user’s guide. Available at http://www.iro.umontreal.ca/ ∼ lecuyer.
L’Ecuyer P, Granger-Piché J (2003) Combined generators with components from different families. Math Comput Simul 62: 395–404
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 169–193
L’Ecuyer P, Simard R (2007) TestU01: a C library for empirical testing of random number generators. ACM Trans Math Softw 33(4):22
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):1073–1075
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 683–689
Marsaglia G (1996) DIEHARD: a battery of tests of randomness. http://www.stat.fsu.edu/pub/diehard. Accessed 3 Aug 2010
Matsumoto M, Nishimura T (1998) Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8(1):3–30
Panneton F, L’Ecuyer P, Matsumoto M (2006) Improved long-period generators based on linear recurrences modulo 2. ACM Trans Math Softw 32(1):1–16
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L’Ecuyer, P. (2011). Uniform Random Number Generators. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_602
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