Intrinsic relations in the structure of linear congruential generators modulo 2β

Ora E. Percus; J. K. Percus

doi:10.1016/0167-7152(92)90158-2

Intrinsic relations in the structure of linear congruential generators modulo 2^β

Ora E. Percus, J. K. Percus

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive two different general relationships that exist among terms of the linear congruential generator x_i+₁ = ax_i + b mod 2^β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

Original language	English (US)
Pages (from-to)	381-383
Number of pages	3
Journal	Statistics and Probability Letters
Volume	15
Issue number	5
DOIs	https://doi.org/10.1016/0167-7152(92)90158-2
State	Published - Dec 8 1992

Keywords

Monte Carlo simulation
Random number generator
linear congruential generator
long range corelations

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1016/0167-7152(92)90158-2

Cite this

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title = "Intrinsic relations in the structure of linear congruential generators modulo 2β",

abstract = "We derive two different general relationships that exist among terms of the linear congruential generator xi+1 = axi + b mod 2β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.",

keywords = "Monte Carlo simulation, Random number generator, linear congruential generator, long range corelations",

author = "Percus, {Ora E.} and Percus, {J. K.}",

note = "Funding Information: This work was supported in part by Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DE-FG02-88ER25052, in part under National Science Foundation, grants ASC 9121428, DMS 9014731, and in part under NATO Grant for International Collaboration CRG 900661.",

year = "1992",

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T1 - Intrinsic relations in the structure of linear congruential generators modulo 2β

AU - Percus, Ora E.

AU - Percus, J. K.

N1 - Funding Information: This work was supported in part by Applied Mathematical Sciences Program of the U.S. Department of Energy under Contract DE-FG02-88ER25052, in part under National Science Foundation, grants ASC 9121428, DMS 9014731, and in part under NATO Grant for International Collaboration CRG 900661.

PY - 1992/12/8

Y1 - 1992/12/8

N2 - We derive two different general relationships that exist among terms of the linear congruential generator xi+1 = axi + b mod 2β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

AB - We derive two different general relationships that exist among terms of the linear congruential generator xi+1 = axi + b mod 2β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

KW - Monte Carlo simulation

KW - Random number generator

KW - linear congruential generator

KW - long range corelations

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