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Binomial random variate generation

Authors:

Voratas Kachitvichyanukul,

Bruce W. SchmeiserAuthors Info & Claims

Communications of the ACM, Volume 31, Issue 2

Pages 216 - 222

https://doi.org/10.1145/42372.42381

Published: 01 February 1988 Publication History

Abstract

Existing binomial random-variate generators are surveyed, and a new generator designed for moderate and large means is developed. The new algorithm, BTPE, has fixed memory requirements and is faster than other such algorithms, both when single, or when many variates are needed.

References

[1]

Abramowitz, M., and Stegun, I.A. Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55, June 1964.

[2]

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

[3]

Ahrens, J.H., and Dieter, U. Sampling from binomial and poisson distributions: A method with bounded computation times, Computing 25, 1980, 193-208.

[4]

Ahrens, J.H., and Dieter, U. Computer generation of poisson deviates from modified normal distributions, ACM Transactions of Mathematical Software 8, 1980. 163-179.

Digital Library

[5]

Atkinson, A.C. The computer generation of poisson random variables, Applied Statistics 28, 1, 1979, 29-35.

[6]

Atkinson, A.C. Recent developments in the computer generation of poisson random variables, Applied Statistics 28, 3, 1979, 260-263.

[7]

Bratley, P., Fox. B.L., and Schrage, L.E. A Guide to Simulation. Springer-Verlag, New York, 1983.

Digital Library

[8]

Chen, H.C., and Asau, Y. On generating random variates from an empirical distribution, AIIE Transactions 6, 1974, 163-166.

[9]

Cheng, R.C.H. Generating beta variates with non-integral shape parameters, Communications of tile ACM 21, 4, (April 1978), 317-322.

Digital Library

[10]

Devroye, L. The computer generation of poisson random variables, Computing 26, 1981, 197-207.

[11]

Devroye, L. "The Computer Generation of Binomial Random Variables,'' Technical Report, McGill University, Montreal, Quebec, Canada, 1980.

[12]

Devroye, L. Generating the maximum of independent identically distributed random variables, Computers and Mathematics with Applications 6, 1980, 305-315.

[13]

Devroye, L., and Naderisamani, A. "Binomial Random Variate Generator,'' Technical Report, McGill University, Montreal, Quebec, Canada, 1980.

[14]

Feller, W. An Introduction to Probability Theory and Its Applications, Volume 1, Wiley, New York, 1968.

[15]

Fishman, G.S. Sampling from the poisson distribution on a computer, Computing 17, 1976, 147-156.

[16]

Fishman, G.S. Principles of Discrete Event Simulation, Wiley, New York, 1978.

Digital Library

[17]

Fishman, G.S. Sampling from the binomial distribution on a computer, Journal of the American Statistical Association 74, 366, 1979, 418-423.

[18]

Fishman, G.S., and Moore, L.R. Sampling from a discrete distribution while preserving monotonicity, The American Statistician 38, 3 1984, 219-223.

[19]

Kachitvichyanukul, V., and Schmeiser, B.W. "Binomial Random Variate Generation," Technical Report 83-9, Industrial and Management Engineering, The University of Iowa, 1983.

[20]

Kinderman, A.J., and Ramage, J.G. Computer generation of normal random variables, Journal of the American Statistical Association 71, 356, 1976, 893-896.

[21]

Kronmal, R.A., and Peterson, A.V., Jr. On the alias method for generating random varaibles from a discrete distribution, American Statistician 33, 1979, 214-218.

[22]

Relies, D.A. A simple algorithm for generating binomial random variables when N is large. Journal of the American Statistical Association 67, 1972, 612-613.

[23]

Schmeiser, B.W. "Random Variate Generation: A Survey." In Simulation with Discrete Models: A State-of-the-Art View, T.I. Oren, C.M. Shub, and P.F. Roth (eds.). In Proceedings of the 1980 Winter Simulation Conference, IEEE, 1980, 79-104.

[24]

Schmeiser, B.W. "Random Variate Generation." In Proceedings of the 1981 Winter Simulation Conference, T.I. Oren, C.M. Delfosse, C.S. Shub (eds.), IEEE, 1981, 227-242.

Digital Library

[25]

Schmeiser, B.W, and Babu, A.J.G. Beta variate generation via exponential majorizing functions, Operations Research 28, 4, 1980, 917-926.

Digital Library

[26]

Schmeiser, B.W., and Kachitvichyanukul, V. "Poisson Random Varlate Generation," Research Memorandum 81-4, Purdue University, 1981.

[27]

Schmeiser, B.W., and Kachitvichyanukul, V. "Correlation Induction withou the Inverse Transformation," In Proceedings of the 1986 Winter Simulation Conference, IEEE, 1986, 266-274.

Digital Library

[28]

Walker, A.J. An efficient method for generating discrete random variables with general distributions, ACM Transactions on Mathematical Software 3, 1977, 252-256.

Digital Library

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Buzdalov MSilva SPaquete L(2023)Improving Time and Memory Efficiency of Genetic Algorithms by Storing Populations as Minimum Spanning Trees of PatchesProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3596388(1873-1881)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583133.3596388
Salem M(2023)Bayesian Analysis for Dependent Progressively Censored Weibull Competing Risks Using CopulasInternational Journal of Reliability, Quality and Safety Engineering10.1142/S021853932350020130:05Online publication date: 24-Aug-2023
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Index Terms

Binomial random variate generation
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Random number generation
    2. Statistical paradigms
      1. Statistical graphics

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Published In

cover image Communications of the ACM

Communications of the ACM Volume 31, Issue 2

Feb. 1988

118 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/42372

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 February 1988

Published in CACM Volume 31, Issue 2

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https://doi.org/10.1038/s42005-024-01648-z
Buzdalov MSilva SPaquete L(2023)Improving Time and Memory Efficiency of Genetic Algorithms by Storing Populations as Minimum Spanning Trees of PatchesProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3596388(1873-1881)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583133.3596388
Salem M(2023)Bayesian Analysis for Dependent Progressively Censored Weibull Competing Risks Using CopulasInternational Journal of Reliability, Quality and Safety Engineering10.1142/S021853932350020130:05Online publication date: 24-Aug-2023
https://doi.org/10.1142/S0218539323500201
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