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Long-range correlation analysis of the Wichmann-Hill random number generator

Abstract

The distribution of points (r n,r n+s), n = 0, 1, 2,...whose coordinates are terms at distance s of the pseudorandom sequence generated by the Wichmann and Hill method is studied. It is known that for many congruential generators critical values of the distance s exist such that these points, far from being uniformly distributed, are concentrated on very few lines. An algorithm is described for computing the critical distances within the Wichmann-Hill sequence and the results obtained are compared with those of other linear congruential generators.

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De Matteis, A., Pagnutti, S. Long-range correlation analysis of the Wichmann-Hill random number generator. Stat Comput 3, 67–70 (1993). https://doi.org/10.1007/BF00153065

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  • DOI: https://doi.org/10.1007/BF00153065

Keywords

  • Pseudorandom numbers
  • compound congruential method
  • Wichmann-Hill generator
  • long-range correlations
  • critical distances