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Efficient table-free sampling methods for the exponential, Cauchy, and normal distributions

Authors:

Joachim H. Ahrens,

Ulrich DieterAuthors Info & Claims

Communications of the ACM, Volume 31, Issue 11

Pages 1330 - 1337

https://doi.org/10.1145/50087.50094

Published: 01 November 1988 Publication History

Abstract

Three algorithms for sampling from exponential, Cauchy and normal distributions are developed. They are based on the "exact approximation" method, and their expected numbers of consumed uniform deviates are less than 1.04 per sample from the target distributions. The algorithms are simple and easily implemented in any desired precision. They require no space for long tables of auxiliary vectors, merely a few constants are needed. Nevertheless, their speed compares well with the performance of much more complex and table-aided sampling procedures.

References

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Ahrens, J.H., and Dieter, U. Extensions of Forsythe's method for random sampling from the normal distribution. Math. Cornp. 27, 124 (Oct. 1973), 927-937.

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Ahrens, J.H., and Dieter, U. Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing 12, (1974), 223-246.

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Ahrens, J.H., and Dieter, U. Sampling from binomiai and Poisson distributions: a method with bounded computation times. Computing 25, (1980), 193-208.

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Cited By

Dunn WShultis J(2023)Some Common Probability DistributionsExploring Monte Carlo Methods10.1016/B978-0-12-819739-4.00019-6(447-495)Online publication date: 2023
https://doi.org/10.1016/B978-0-12-819739-4.00019-6
Dražić Z(2023)Fat-tailed distributions for continuous variable neighborhood searchOptimization Letters10.1007/s11590-023-01999-617:9(2299-2320)Online publication date: 3-Apr-2023
https://doi.org/10.1007/s11590-023-01999-6
Cybulski R(2021)Pseudo-random number generator based on linear congruence and delayed Fibonacci methodTechnical Sciences10.31648/ts.7238Online publication date: 6-Dec-2021
https://doi.org/10.31648/ts.7238
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Index Terms

Efficient table-free sampling methods for the exponential, Cauchy, and normal distributions
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Statistical graphics

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Published In

cover image Communications of the ACM

Communications of the ACM Volume 31, Issue 11

Nov. 1988

102 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/50087

Editor:
Peter J. Denning
NASA Ames Research Center, Moffett Field, CA

Issue’s Table of Contents

Copyright © 1988 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 1988

Published in CACM Volume 31, Issue 11

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Cited By

Dunn WShultis J(2023)Some Common Probability DistributionsExploring Monte Carlo Methods10.1016/B978-0-12-819739-4.00019-6(447-495)Online publication date: 2023
https://doi.org/10.1016/B978-0-12-819739-4.00019-6
Dražić Z(2023)Fat-tailed distributions for continuous variable neighborhood searchOptimization Letters10.1007/s11590-023-01999-617:9(2299-2320)Online publication date: 3-Apr-2023
https://doi.org/10.1007/s11590-023-01999-6
Cybulski R(2021)Pseudo-random number generator based on linear congruence and delayed Fibonacci methodTechnical Sciences10.31648/ts.7238Online publication date: 6-Dec-2021
https://doi.org/10.31648/ts.7238
Holohan NBraghin S(2021)Secure Random Sampling in Differential PrivacyComputer Security – ESORICS 202110.1007/978-3-030-88428-4_26(523-542)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1007/978-3-030-88428-4_26
Dyer J(2016)Monte Carlo Simulation Design for Evaluating Normal-Based Control Chart PropertiesJournal of Modern Applied Statistical Methods10.22237/jmasm/147800358015:2(580-626)Online publication date: 1-Nov-2016
https://doi.org/10.22237/jmasm/1478003580
Agbormbai A(2012)Efficient Sampling Schemes for DSMC Computations8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference10.2514/6.2002-2762Online publication date: 25-Jun-2012
https://doi.org/10.2514/6.2002-2762
Wiebke JPahl ESchwerdtfeger P(2012)Up to fourth virial coefficients from simple and efficient internal-coordinate sampling: Application to neonThe Journal of Chemical Physics10.1063/1.4731344137:1Online publication date: 5-Jul-2012
https://doi.org/10.1063/1.4731344
Carrizosa EDraić MDraić ZMladenović N(2012)Gaussian variable neighborhood search for continuous optimizationComputers and Operations Research10.1016/j.cor.2011.11.00339:9(2206-2213)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1016/j.cor.2011.11.003
(2012)Some Common Probability DistributionsExploring Monte Carlo Methods10.1016/B978-0-444-51575-9.00011-7(307-336)Online publication date: 2012
https://doi.org/10.1016/B978-0-444-51575-9.00011-7
Tanizaki H(2009)Random Number Generation IComputational Methods in Statistics and Econometrics10.1201/9780203022023.pt1Online publication date: 14-Dec-2009
https://doi.org/10.1201/9780203022023.pt1
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