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Computer generation of gamma random variables—II

Author:

Pandu R. TadikamallaAuthors Info & Claims

Communications of the ACM, Volume 21, Issue 11

Pages 925 - 928

https://doi.org/10.1145/359642.359648

Published: 01 November 1978 Publication History

Abstract

A rejection method is proposed for generating gamma variates with nonintegral shape parameter α, α > 1. This method is similar to other methods given by Fishman, Wallace, and Tadikamalla and is faster than these methods for α > 2. The core storage requirements and the programming effort for the proposed method are similar to those of Wallace's or Tadikamalla's methods. The computational times for the proposed method remain fairly constant for medium and large values of α and are superior to times obtained by Arhens and Dieter's method for all values of α. The proposed method is simpler than Ahrens and Dieter's method.

References

[1]

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

[2]

Atkinson, A.C., and Pearce, M.C. The computer generation of beta gamma and normal random variables. J. Royal Statist. Soc. Ser. A, 139 (1976), 431-461.

[3]

Box, G.E.P., and Muller, M.E. A note on the generation of normal deviates. Annals Math. Statist. 29 (1958), 610-611.

[4]

Dudewicz, E.J. Speed and quality of random numbers. Annual Tech. Conf. Trans. ASQC, Vol. 29, 1975, pp. 170-180.

[5]

Fishman, G.S. Sampling from the gamma distribution on a computer. Comm. ACM. 19, 7 (July 1976), 407-409.

Digital Library

[6]

Greenwood, A.J. A fast generator for gamma distributed random variables. In CompStat, G. Bruckman et al., Eds., Physica Verlag, Vienna, 1974, pp. 19-27.

[7]

Johnk, M.D. Erzeugung Von Betavesteilten Und Gamma Vesteilten Zufellszahlen. Metrika 8 (1964), 5-15.

[8]

Kinderman, A.J., and Ramage, J.G. Computer generation of normal random variables. J. Amer. Statist. Assoc. 17 (1976), 893-896.

[9]

Lurie, D., and Mason, R.L. Empirical investigation of several techniques for computer generation of order statistics. Comm. Statist. 2 (1973), 363-371.

[10]

Marsaglia, G. Random variables and computer. Trans. Third Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, June 1962, Prague: Czechoslovak Acad. of Sciences, Prague, 1964, pp. 499-512.

[11]

Odell, P.L., and Newman, T.G. The Generation of Random Variates. Charles Griffin, London, 1972.

[12]

Tadikamalla, P.R. Computer generation of gamma random variables. Comm. ACM 21, 5 (May 1978), 419-422.

Digital Library

[13]

Tadikamalla, P.R. FORTRAN programs for computer generation of gamma random variables. Tech. Rep., Dept. Business Admin., Eastern Kentucky U., Richmond, Ky., 1977.

[14]

Tadikamalla, P.R. The factors that may affect the speed of normal variate generators. Tech. Rep., Dept. Business Admin., Eastern Kentucky U., Richmond, Ky., 1978.

[15]

Tadikamalla, P.R., and Johnson, M.E. Some simple rejection methods for sampling from the normal distribution. Proc. First Int. Conf. Math. Modeling, St. Louis, Mo., 1977, 573-578.

[16]

Wallace, N.D. Computer generation of gamma random variates with non-integral shape parameters. Comm. ACM 17, 12 (Dec. 1974), 691-695.

Digital Library

[17]

Whittekar, J. Generating gamma and beta random variables with nonintegral shape parameters. App. Statist. 23 (1974), 210-213.

Cited By

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Index Terms

Computer generation of gamma random variables—II
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation

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Copyright © 1978 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 1978

Published in CACM Volume 21, Issue 11

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Luengo E(2022)Gamma Pseudo Random Number GeneratorsACM Computing Surveys10.1145/352715755:4(1-33)Online publication date: 21-Nov-2022
https://dl.acm.org/doi/10.1145/3527157
Li DZhong J(2020)Dimensionally Aware Multi-Objective Genetic Programming for Automatic Crowd Behavior ModelingACM Transactions on Modeling and Computer Simulation10.1145/339140730:3(1-24)Online publication date: 5-Jul-2020
https://dl.acm.org/doi/10.1145/3391407
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https://dl.acm.org/doi/10.1145/3379489
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Hornbæk K(2015)We must be more wrong in HCI researchInteractions10.1145/283309322:6(20-21)Online publication date: 28-Oct-2015
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