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On the statistical independence of nonlinear congruential pseudorandom numbers

Editor: Richard E. Nance Authors:

Jürgen Eichenauer-Herrmann,

Harald NiederreiterAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 4, Issue 1

Pages 89 - 95

https://doi.org/10.1145/174619.174622

Published: 01 January 1994 Publication History

Abstract

Recently, several nonlinear congruential methods for generating uniform pseudorandom numbers have been proposed and analysed. In the present note, further statistical independence properties of a general class of nonlinear congruential pseudorandom number generators are established. The results that are obtained are essentially best possible in an asymptotic sense and show that the generated pseudorandom numbers model truly random numbers very closely in terms of asymptotic discrepancy.

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EICHENAUER, J., GROTHE, H., AND LEHN, J. 1988. Marsaglia's lattice test and non-linear congruential pseudo random number generators. Metrika 35, 241-250.

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NmDERRErTER, H. 1992b. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, Penn.

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Cited By

Mansharamani RKallepalli PVeerabhadraiah HMathew B(2014)RVGEN: a tool for generation of random variatesSoftware - Concepts & Tools10.1007/s00378990000219:4(161-167)Online publication date: 3-May-2014
https://doi.org/10.1007/s003789900002
Eichenauer-Herrmann JHerrmann EWegenkittl S(2011)A survey of quadratic and inversive congruential pseudorandom numbersMonte Carlo and Quasi-Monte Carlo Methods 199610.1007/978-1-4612-1690-2_4(66-97)Online publication date: 23-May-2011
https://doi.org/10.1007/978-1-4612-1690-2_4
Eichenauer-Herrmann JLarcher G(1996)Average Behaviour of Compound Nonlinear Congruential Pseudorandom NumbersFinite Fields and Their Applications10.1006/ffta.1996.00082:1(111-123)Online publication date: 1-Jan-1996
https://dl.acm.org/doi/10.1006/ffta.1996.0008
Show More Cited By

Index Terms

On the statistical independence of nonlinear congruential pseudorandom numbers
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Random number generation

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Reviews

Reviewer: Prokop Vondracek

The standard method of generating uniform pseudorandom numbers is the linear congruential method. This method shows a lot of undesirable regularities, however, which led to the development of several nonlinear congruential methods. The authors review recent work in this area and establish further statistical independence properties of a general class of nonlinear congruential pseudorandom number generators.

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Published In

cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 4, Issue 1

Jan. 1994

129 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/174619

Editor:
Richard E. Nance
Virginia Tech, Blacksburg

Issue’s Table of Contents

Copyright © 1994 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1994

Published in TOMACS Volume 4, Issue 1

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Cited By

Mansharamani RKallepalli PVeerabhadraiah HMathew B(2014)RVGEN: a tool for generation of random variatesSoftware - Concepts & Tools10.1007/s00378990000219:4(161-167)Online publication date: 3-May-2014
https://doi.org/10.1007/s003789900002
Eichenauer-Herrmann JHerrmann EWegenkittl S(2011)A survey of quadratic and inversive congruential pseudorandom numbersMonte Carlo and Quasi-Monte Carlo Methods 199610.1007/978-1-4612-1690-2_4(66-97)Online publication date: 23-May-2011
https://doi.org/10.1007/978-1-4612-1690-2_4
Eichenauer-Herrmann JLarcher G(1996)Average Behaviour of Compound Nonlinear Congruential Pseudorandom NumbersFinite Fields and Their Applications10.1006/ffta.1996.00082:1(111-123)Online publication date: 1-Jan-1996
https://dl.acm.org/doi/10.1006/ffta.1996.0008
Niederreiter H(1995)New Developments in Uniform Pseudorandom Number and Vector GenerationMonte Carlo and Quasi-Monte Carlo Methods in Scientific Computing10.1007/978-1-4612-2552-2_5(87-120)Online publication date: 1995
https://doi.org/10.1007/978-1-4612-2552-2_5

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