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Checking the quality of approximation of p-values in statistical tests for random number generators by using a three-level test

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  • Haramoto, Hiroshi
  • Matsumoto, Makoto

Abstract

Statistical tests of pseudorandom number generators (PRNGs) are applicable to any type of random number generators and are indispensable for evaluation. While several practical packages for statistical tests of randomness exist, they may suffer from a lack of reliability: for some tests, the amount of approximation error can be deemed significant. Reducing this error by finding a better approximation is necessary, but it generally requires an enormous amount of effort. In this paper, we introduce an experimental method for revealing defects in statistical tests by using a three-level test proposed by Okutomi and Nakamura. In particular, we investigate the NIST test suite and the test batteries in TestU01, which are widely used statistical packages. Furthermore, we show the efficiency of several modifications for some tests.

Suggested Citation

  • Haramoto, Hiroshi & Matsumoto, Makoto, 2019. "Checking the quality of approximation of p-values in statistical tests for random number generators by using a three-level test," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 66-75.
    • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:66-75
    DOI: 10.1016/j.matcom.2018.08.005
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    References listed on IDEAS

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    1. Pierre L'Écuyer & Jean-François Cordeau & Richard Simard, 2000. "Close-Point Spatial Tests and Their Application to Random Number Generators," Operations Research, INFORMS, vol. 48(2), pages 308-317, April.
    2. Simard, Richard & L'Ecuyer, Pierre, 2011. "Computing the Two-Sided Kolmogorov-Smirnov Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i11).
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