Skip to main content
SpringerLink
Log in

Modified explicit inversive congruential pseudorandom numbers with power of 2 modulus

  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

A modified version of the explicit inversive congruential method with power of 2 modulus for generating uniform pseudorandom numbers is introduced. The statistical independence behaviour of the generated sequences is studied based on the distribution of all pairs of successive pseudorandom numbers over the entire period. Lower and upper bounds for the discrepancy of the corresponding two-dimensional point sets are established. These results certainly play only a minor part in studying the statistical independence behaviour of the generated sequences, but they show that modified explicit inversive congruential pseudorandom numbers have some attractive properties at least regarding their two-dimensional discrepancy. The method of proof relies heavily on a thorough analysis of certain exponential sums.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Eichenauer-Herrmann, J. (1992) Inversive congruential pseudorandom numbers: a tutorial. International Statistical Review, 60, 167–176.

    Google Scholar 

  • Eichenauer-Herrmann, J. (1995) Pseudorandom number generation by nonlinear methods. International Statistical Review (to appear).

  • Eichenauer-Herrmann, J. and Ickstadt, K. (1994) Explicit inversive congruential pseudorandom numbers with power of two modulus. Mathematics of Computation, 62, 787–797.

    Google Scholar 

  • Eichenauer-Herrmann, J. and Niederreiter, H. (1993) Kloostermantype sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers. Acta Arithmetica, 65, 185–194.

    Google Scholar 

  • Kiefer, J. (1961) On large deviations of the empiric d.f. of vector chance variables and a law of the interated logarithm. Pacific Journal of Mathematics, 11, 649–660.

    Google Scholar 

  • Niederreiter, H. (1989) The serial test for congruential pseudorandom numbers generated by inversions. Mathematics of Computation, 52, 135–144.

    Google Scholar 

  • Niederreiter, H. (1992) Random Number Generation and Quasi Monte Carlo Methods, SIAM, Philadelphia.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289, Darmstadt, Germany

    Jürgen Eichenauer-Herrmann

Authors
  1. Jürgen Eichenauer-Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eichenauer-Herrmann, J. Modified explicit inversive congruential pseudorandom numbers with power of 2 modulus. Stat Comput 6, 31–36 (1996). https://doi.org/10.1007/BF00161571

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00161571

Keywords

Search

Navigation