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Geometric and Statistical Properties of Pseudorandom Number Generators Based on Multiple Recursive Transformations

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Monte Carlo and Quasi-Monte Carlo Methods 2010

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 23))

Abstract

The equidistribution property is studied for the generators of the MRG type. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, including detailed study of its geometric and statistical properties, in particular, proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, 142432, Chernogolovka, Russia

    L. Yu. Barash

Authors
  1. L. Yu. Barash
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Correspondence to L. Yu. Barash .

Editor information

Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Barash, L.Y. (2012). Geometric and Statistical Properties of Pseudorandom Number Generators Based on Multiple Recursive Transformations. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_12

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