article

Beta Variate Generation via Exponential Majorizing Functions

Authors: Bruce W. Schmeiser, A. J. G. BabuAuthors Info & Claims

Pages 917 - 926

https://doi.org/10.1287/opre.28.4.917

Published: 01 August 1980 Publication History

Abstract

Two acceptance/rejection algorithms for generating random variates from the beta distribution are developed. The algorithms use piece-wise linear and exponential majorizing functions coupled with a piece-wise linear minorizing function. The algorithms are exact to within the accuracy of the computer and are valid for all parameter values greater than one Marginal execution times are relatively insensitive to parameter values and are faster than any previously published algorithms.

References

[1]

J. H. AHRENS AND U. DIETER, "Computer Methods for Sampling from Gamma, Beta, Poisson and Binomial Distributions," Computing 12, 223- 246 (1974).

Crossref

Google Scholar

[2]

A. C. ATKINSON AND M. C. PEARCE, "The Computer Generation of Beta, Gamma and Normal Random Variables." J. R. Statist. Soc. A 139, 431- 461 (1976).

Crossref

Google Scholar

[3]

A. C. ATKINSON AND J. WHITTAKER, "A Switching Algorithm for the Generation of Beta Random Variables with at Least One Parameter Less than 1," J. R. Statist. Soc. A 139, 462-467 (1976).

Crossref

Google Scholar

[4]

R. C. H. CHENG, "Generating Beta Variates with Nonintegral Shape Parameters," Communications ACM 21, 317-322 (1978).

Digital Library

Google Scholar

[5]

G. E. FORSYTHE, "Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions," Math. Comput. 26, 817- 826 (1972).

Google Scholar

[6]

B. L. Fox, "Generation of Random Samples from the Beta and F Distributions," Technometrics 5, 269-270 (1963).

Crossref

Google Scholar

[7]

D. LURIE AND H. O. HARTLEY, "Machine-generation of Order Statistics for Monte Carlo Computations," Am. Statist. 26, 26-27 (1972).

Google Scholar

[8]

M. D. JOHNK, "Erzeugung von Betaverteilten und Gammaverteilten Zufallszahlen," Metrika 8, 5-15 (1964).

Crossref

Google Scholar

[9]

B. W. SCHMEISER AND M. A. SHALABY, "Acceptance/Rejection Methods for Beta Variate Generation," J. Am. Statist. Assoc. 75, 371 (1980).

Google Scholar

[10]

B. W. SCHMEISER, "Generation of Variates from Distribution Tails," Opns. Res. 28, 1011-1016 (1980).

Digital Library

Google Scholar

[11]

W. R. SCHUCANY, "Order Statistics in Simulation," J. Statist. Comput. Simulation 1, 281-286 (1972).

Crossref

Google Scholar

[12]

J. WHITTAKER, "Generating Gamma and Beta Random Variables with Nonintegral Shape Parameters," Appl. Statist. 23, 210-214 (1974).

Crossref

Google Scholar

Cited By

View all

Kuhl M(2017)History of random variate generationProceedings of the 2017 Winter Simulation Conference10.5555/3242181.3242196(1-12)Online publication date: 3-Dec-2017
https://dl.acm.org/doi/10.5555/3242181.3242196
Cheng CHung YBalakrishnan N(2014)Generating beta random numbers and Dirichlet random vectors in RComputational Statistics & Data Analysis10.5555/2749482.274985171:C(1011-1020)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.5555/2749482.2749851
Devroye LJames L(2011)The double CFTP methodACM Transactions on Modeling and Computer Simulation10.1145/1899396.189939821:2(1-20)Online publication date: 18-Feb-2011
https://dl.acm.org/doi/10.1145/1899396.1899398
Show More Cited By

Recommendations

Singular matrix variate beta distribution

In this paper, we determine the symmetrised density of doubly noncentral singular matrix variate beta type I and II distributions under different definitions. As particular cases we obtain the noncentral singular matrix variate beta type I and II ...
Extended matrix variate gamma and beta functions

The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In ...
Efficient matrix-exponential random variate generation using a numeric linear combination approach
DEVS '14: Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS Integrative

Matrix Exponential (ME) probability distributions form a versatile family of distributions and enable an accurate description and simulation of a wide variety of situations where a positive distribution is required. In queueing theory they are used for ...

Comments

Information & Contributors

Information

Published In

Operations Research Volume 28, Issue 4

August 1980

181 pages

ISSN:0030-364X

Issue’s Table of Contents

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 August 1980

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 12 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Kuhl M(2017)History of random variate generationProceedings of the 2017 Winter Simulation Conference10.5555/3242181.3242196(1-12)Online publication date: 3-Dec-2017
https://dl.acm.org/doi/10.5555/3242181.3242196
Cheng CHung YBalakrishnan N(2014)Generating beta random numbers and Dirichlet random vectors in RComputational Statistics & Data Analysis10.5555/2749482.274985171:C(1011-1020)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.5555/2749482.2749851
Devroye LJames L(2011)The double CFTP methodACM Transactions on Modeling and Computer Simulation10.1145/1899396.189939821:2(1-20)Online publication date: 18-Feb-2011
https://dl.acm.org/doi/10.1145/1899396.1899398
Stadlober EZechner H(1999)The patchwork rejection technique for sampling from unimodal distributionsACM Transactions on Modeling and Computer Simulation10.1145/301677.3016859:1(59-80)Online publication date: 1-Jan-1999
https://dl.acm.org/doi/10.1145/301677.301685
Kachitvichyanukul VSchmeiser B(1988)Binomial random variate generationCommunications of the ACM10.1145/42372.4238131:2(216-222)Online publication date: 1-Feb-1988
https://dl.acm.org/doi/10.1145/42372.42381
Schmeiser BKachitvichyanukul V(1986)Correlation induction without the inverse transformationProceedings of the 18th conference on Winter simulation10.1145/318242.318445(266-274)Online publication date: 1-Dec-1986
https://dl.acm.org/doi/10.1145/318242.318445

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

Singular matrix variate beta distribution

Extended matrix variate gamma and beta functions

Efficient matrix-exponential random variate generation using a numeric linear combination approach

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations