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On the Distribution of Some New Explicit Inversive Pseudorandom Numbers and Vectors

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

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  • Arne Winterhof

    (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)

Abstract

Summary Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the new explicit inversive method recently introduced by Meidl and the author. We present nontrivial results on the distribution of pseudorandom numbers and vectors generated by this method over the full period and in parts of the period. Moreover, we establish some new results on the statistical properties of parallel streams of such pseudorandom numbers. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties. The proofs are based on new bounds on certain exponential sums over finite fields.

Suggested Citation

  • Arne Winterhof, 2006. "On the Distribution of Some New Explicit Inversive Pseudorandom Numbers and Vectors," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 487-499, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_30
    DOI: 10.1007/3-540-31186-6_30
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