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Random number generation

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  • L'Ecuyer, Pierre

Abstract

The fields of probability and statistics are built over the abstract concepts of probability space and random variable. This has given rise to elegant and powerful mathematical theory, but exact implementation of these concepts on conventional computers seems impossible. In practice, random variables and other random objects are simulated by deterministic algorithms. The purpose of these algorithms is to produce sequences of numbers or objects whose behavior is very hard to distinguish from that of their ?truly random? counterparts, at least for the application of interest. Key requirements may differ depending on the context. For Monte Carlo methods, the main goal is to reproduce the statistical properties on which these methods are based, so that the Monte Carlo estimators behave as expected, whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random.

Suggested Citation

  • L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    • Handle: RePEc:zbw:caseps:200421
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    File URL: https://www.econstor.eu/bitstream/10419/22195/1/21_pl.pdf
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    References listed on IDEAS

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    1. L’Ecuyer, Pierre & Simard, Richard, 2001. "On the performance of birthday spacings tests with certain families of random number generators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 131-137.
    2. L'Ecuyer, Pierre & Andres, Terry H., 1997. "A random number generator based on the combination of four LCGs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(1), pages 99-107.
    3. L’Ecuyer, Pierre & Granger-Piché, Jacinthe, 2003. "Combined generators with components from different families," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 395-404.
    4. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784, Decembrie.
    5. Pierre L'Ecuyer & Raymond Couture, 1997. "An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 9(2), pages 206-217, May.
    6. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
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    2. Li, Shuaiyu & Wu, Yunpei & Cheng, Yuzhong, 2024. "Parameter estimation and random number generation for student Lévy processes," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

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