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Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates

Abstract

Systematic patterns are revealed when sequences of pseudo-random uniform deviates are generated from multiplicative congruential generators. If the initial seeds, x 0 and y 0, for two such sequences are related by y 0 = (n 1/n 2)x 0, where n 1 and n 2 are relatively prime, positive integers, then an approximate argument suggests that the asymptotic correlation coefficient between corresponding members of the two sequences is (n 1 n 2)−1. This unsettling phenomenon is discussed in the context of related, existing literature.

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References

  • Afflerbach, L. and Grothe, H. (1988) The lattice structure of pseudo-random vectors generated by matrix generators. J. Comput. Appl. Math., 23, 127–131.

    Google Scholar 

  • De Matteis, A. and Pagnutti, S. (1988) Parallelization of random number generators and long-range correlations. Numer. Math., 53, 595–608.

    Google Scholar 

  • De Matteis, A. and Pagnutti, S. (1990) Long-range correlations in linear and non-linear random number generators. Parall. Comp., 14, 207–210.

    Google Scholar 

  • Durst, M. J. (1989) Using linear congruential generators for parallel random number generation. Proc. 1989 Winter Simulation Conf., pp. 462–466. IEEE Press.

  • Eichenauer-Herrmann, J., Grothe, H. and Lehn, J. (1989) On the period length of pseudo-random vector sequences generated by matrix generators. Math. Comput., 52, 145–148.

    Google Scholar 

  • Fishman, G. S. and Moore, L. R. (1982) A statistical evaluation of multiplicative congruential random number generators with modulus 231 − 1. J. Amer. Statist. Assoc., 77, 129–136.

    Google Scholar 

  • Grothe, H. (1987) Matrix generators for pseudo-random vector generation. Statistische Hefte, 28, 233–238.

    Google Scholar 

  • James, F. (1990) A review of pseudorandom number generators. Comput. Phys. Commun., 60, 329–344.

    Google Scholar 

  • Knuth, D. E. (1981) The Art of Computer Programming Volume 2: Seminumerical Algorithms, 2nd edn. Addison-Wesley, Reading, MA.

    Google Scholar 

  • l'Ecuyer, P. (1990) Random numbers for simulation. Commun. ACM, 33, 85–98.

    Google Scholar 

  • Maclaren, N. M. (1989) The generation of multiple independent sequences of pseudorandom numbers. Appl. Statist., 38, 351–359.

    Google Scholar 

  • NAg (1989) FORTRAN Subroutine Library, Mark 13, Numerical Algorithms Group, Oxford.

    Google Scholar 

  • Naus, J. I. (1965a) The distribution of the size of the maximum cluster of points on a line. J. Amer. Statist. Assoc., 60, 532–538.

    Google Scholar 

  • Naus, J. I. (1965b) Clustering of random points in two dimensions. Biometrika, 52, 263–267.

    Google Scholar 

  • Ripley, B. D. (1987) Stochastic Simulation. Wiley, New York.

    Google Scholar 

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Anderson, N.H., Titterington, D.M. Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates. Stat Comput 3, 61–65 (1993). https://doi.org/10.1007/BF00153064

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  • DOI: https://doi.org/10.1007/BF00153064

Keywords

  • Cross-correlation
  • congruential generators
  • uniform deviates