Long range correlations in linear congruential generators
type: Item
instance of: scholarly article
title: Long range correlations in linear congruential generators
zbMATH Open document ID: 0644.65003
DOI: 10.1016/0021-9991(88)90166-0
author: Ora E. Percus
author: Jerome K. Percus
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: Different methods for generating sequences \(\{\) X(n)\(|\) \(n\in N\}\) of independently and uniformly distributed random numbers are proposed in the literature. The simple linear congruential generator \(X(n)\equiv a.X(n-1)+b\) (mod M) is recommended especially for use in mini and microcomputers. The parameters a, b (and sometimes M) are chosen to ensure the randomness of the sequence \(\{\) X(n)\(|\) \(n\in N\}.\) In this paper the authors study the case \(M=2\) d. They establish that for a fixed k, among the terms \(X(n+j.2\) k), \(1\leq j\leq p\), there exists a linear relation \(\sum^{p}_{j=0}c_ j.X(n+j.2\quad k)\equiv 0\) (mod 2 d). Therefore a linear congruential generator (with \(M=2\) d) introduces correlations among elements separated sequentially by powers of two. Hence more care must be taken for Monte Carlo procedures; the authors suggest to skip members of the sequence \(\{\) X(n)\(\}\) or to do a random change for the parameter b.
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 4050835
zbMATH Keywords: linear congruential generator
zbMATH Keywords: microcomputers
zbMATH Keywords: correlations
zbMATH Keywords: Monte Carlo
reviewed by: V.S.Stefănescu
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90166-0
OpenAlex ID: W2025718386
cites work: Q3935355
cites work: Q3259107
description: scientific article; zbMATH DE number 4050835