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On the performance of birthday spacings tests with certain families of random number generators

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  • L’Ecuyer, Pierre
  • Simard, Richard

Abstract

We examine how a statistical test based on discrete spacings between points, in one or more dimensions, detects the regularities in certain popular classes of random number generators. We provide a rule of thumb giving the minimal sample size for the test to reject the generator systematically, as a function of the generator’s size (or period length), for generator families such as the linear congruential, Taus worthe, non linear inversive, etc. Full period linear congruential generators with a good behavior in the spectral test, for example, start to fail the two-dimensional test decisively at sample sizes approximately equal to the cubic root of their period length (or modulus).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:55:y:2001:i:1:p:131-137
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Pierre L'Ecuyer & Richard Simard & E. Jack Chen & W. David Kelton, 2002. "An Object-Oriented Random-Number Package with Many Long Streams and Substreams," Operations Research, INFORMS, vol. 50(6), pages 1073-1075, December.
    2. Michael S. Delgado & Christopher F. Parmeter, 2013. "Embarrassingly Easy Embarrassingly Parallel Processing in R: Implementation and Reproducibility," Working Papers 2013-06, University of Miami, Department of Economics.
    3. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    4. 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.
    5. Pierre L'Ecuyer & Richard Simard, 2014. "On the Lattice Structure of a Special Class of Multiple Recursive Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 449-460, August.
    6. Harase, Shin, 2019. "Conversion of Mersenne Twister to double-precision floating-point numbers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 76-83.
    7. Aljahdali Asia & Mascagni Michael, 2017. "Feistel-inspired scrambling improves the quality of linear congruential generators," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 89-99, June.
    8. Pierre L’Ecuyer & Paul Wambergue & Erwan Bourceret, 2020. "Spectral Analysis of the MIXMAX Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 135-144, January.

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