A note on the quality of random variates generated by the ratio of uniforms method

Wolfgang Hörmann

doi:10.57938/6342f44e-2654-4857-802c-f8281ff1dcec

A note on the quality of random variates generated by the ratio of uniforms method

Wolfgang Hörmann

Institute for Statistics and Mathematics

Publication: Working/Discussion Paper › WU Working Paper

29 Downloads (Pure)

Abstract

The one-dimensional distribution of pseudo-random numbers generated by the ratio of uniforms methods using linear congruential generators (LCGs) as the source of uniform random numbers is investigated in this paper. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that the Cauchy the normal or the exponential distribution are generated. These bounds justify the recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract)

Original language	English
Place of Publication	Vienna
Publisher	Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business
DOIs	https://doi.org/10.57938/6342f44e-2654-4857-802c-f8281ff1dcec
Publication status	Published - 1993

Publication series

Series	Preprint Series / Department of Applied Statistics and Data Processing
Number	5

WU Working Paper Series

Preprint Series / Department of Applied Statistics and Data Processing

Access to Document

10.57938/6342f44e-2654-4857-802c-f8281ff1dcecLicence: Unspecified

DocumentFinal published version, 175 KBLicence: Unspecified

Check availability

University Library Catalogue

Cite this

Hörmann, W. (1993). A note on the quality of random variates generated by the ratio of uniforms method. (July 1993 ed.) Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business. Preprint Series / Department of Applied Statistics and Data Processing No. 5 https://doi.org/10.57938/6342f44e-2654-4857-802c-f8281ff1dcec

@techreport{6342f44e26544857802cf8281ff1dcec,

title = "A note on the quality of random variates generated by the ratio of uniforms method",

abstract = "The one-dimensional distribution of pseudo-random numbers generated by the ratio of uniforms methods using linear congruential generators (LCGs) as the source of uniform random numbers is investigated in this paper. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that the Cauchy the normal or the exponential distribution are generated. These bounds justify the recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract)",

author = "Wolfgang H{\"o}rmann",

year = "1993",

doi = "10.57938/6342f44e-2654-4857-802c-f8281ff1dcec",

language = "English",

series = "Preprint Series / Department of Applied Statistics and Data Processing",

number = "5",

publisher = "Institut f{\"u}r Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business",

edition = "July 1993",

type = "WorkingPaper",

institution = "Institut f{\"u}r Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business",

}

Hörmann, W 1993 'A note on the quality of random variates generated by the ratio of uniforms method' Preprint Series / Department of Applied Statistics and Data Processing, no. 5, July 1993 edn, Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna. https://doi.org/10.57938/6342f44e-2654-4857-802c-f8281ff1dcec

TY - UNPB

T1 - A note on the quality of random variates generated by the ratio of uniforms method

AU - Hörmann, Wolfgang

PY - 1993

Y1 - 1993

N2 - The one-dimensional distribution of pseudo-random numbers generated by the ratio of uniforms methods using linear congruential generators (LCGs) as the source of uniform random numbers is investigated in this paper. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that the Cauchy the normal or the exponential distribution are generated. These bounds justify the recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract)

AB - The one-dimensional distribution of pseudo-random numbers generated by the ratio of uniforms methods using linear congruential generators (LCGs) as the source of uniform random numbers is investigated in this paper. Due to the two-dimensional lattice structure of LCGs there is always a comparable large gap without a point in the one-dimensional distribution of any ratio of uniforms method. Lower bounds for these probabilities only depending on the modulus and the Beyer quotient of the LCG are proved for the case that the Cauchy the normal or the exponential distribution are generated. These bounds justify the recommendation not to use the ratio of uniforms method combined with LCGs. (author's abstract)

U2 - 10.57938/6342f44e-2654-4857-802c-f8281ff1dcec

DO - 10.57938/6342f44e-2654-4857-802c-f8281ff1dcec

M3 - WU Working Paper

T3 - Preprint Series / Department of Applied Statistics and Data Processing

BT - A note on the quality of random variates generated by the ratio of uniforms method

PB - Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business

CY - Vienna

ER -