Voratas Kachitvichyanukul
Skip Abstract Section
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.
- 1 Abramowitz, M., and Stegun, I.A. Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55, June 1964.Google Scholar
- 2 Ahrens, J.H., and Dieter, U. Computer methods for sampling from gamma, beta, poisson and binomial distributions, Computing 12, (1974), 223-246.Google ScholarCross Ref
- 3 Ahrens, J.H., and Dieter, U. Sampling from binomial and poisson distributions: A method with bounded computation times, Computing 25, 1980, 193-208.Google ScholarCross Ref
- 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. Google ScholarDigital Library
- 5 Atkinson, A.C. The computer generation of poisson random variables, Applied Statistics 28, 1, 1979, 29-35.Google Scholar
- 6 Atkinson, A.C. Recent developments in the computer generation of poisson random variables, Applied Statistics 28, 3, 1979, 260-263.Google Scholar
- 7 Bratley, P., Fox. B.L., and Schrage, L.E. A Guide to Simulation. Springer-Verlag, New York, 1983. Google ScholarDigital Library
- 8 Chen, H.C., and Asau, Y. On generating random variates from an empirical distribution, AIIE Transactions 6, 1974, 163-166.Google ScholarCross Ref
- 9 Cheng, R.C.H. Generating beta variates with non-integral shape parameters, Communications of tile ACM 21, 4, (April 1978), 317-322. Google ScholarDigital Library
- 10 Devroye, L. The computer generation of poisson random variables, Computing 26, 1981, 197-207.Google ScholarCross Ref
- 11 Devroye, L. "The Computer Generation of Binomial Random Variables,'' Technical Report, McGill University, Montreal, Quebec, Canada, 1980.Google Scholar
- 12 Devroye, L. Generating the maximum of independent identically distributed random variables, Computers and Mathematics with Applications 6, 1980, 305-315.Google ScholarCross Ref
- 13 Devroye, L., and Naderisamani, A. "Binomial Random Variate Generator,'' Technical Report, McGill University, Montreal, Quebec, Canada, 1980.Google Scholar
- 14 Feller, W. An Introduction to Probability Theory and Its Applications, Volume 1, Wiley, New York, 1968.Google Scholar
- 15 Fishman, G.S. Sampling from the poisson distribution on a computer, Computing 17, 1976, 147-156.Google ScholarCross Ref
- 16 Fishman, G.S. Principles of Discrete Event Simulation, Wiley, New York, 1978. Google ScholarDigital Library
- 17 Fishman, G.S. Sampling from the binomial distribution on a computer, Journal of the American Statistical Association 74, 366, 1979, 418-423.Google Scholar
- 18 Fishman, G.S., and Moore, L.R. Sampling from a discrete distribution while preserving monotonicity, The American Statistician 38, 3 1984, 219-223.Google Scholar
- 19 Kachitvichyanukul, V., and Schmeiser, B.W. "Binomial Random Variate Generation," Technical Report 83-9, Industrial and Management Engineering, The University of Iowa, 1983.Google Scholar
- 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.Google ScholarCross Ref
- 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.Google ScholarCross Ref
- 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.Google ScholarCross Ref
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 25 Schmeiser, B.W,, and Babu, A.J.G. Beta variate generation via exponential majorizing functions, Operations Research 28, 4, 1980, 917-926.Google ScholarDigital Library
- 26 Schmeiser, B.W., and Kachitvichyanukul, V. "Poisson Random Varlate Generation," Research Memorandum 81-4, Purdue University, 1981.Google Scholar
- 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. Google ScholarDigital 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. Google ScholarDigital Library
Index Terms
- Binomial random variate generation
Recommendations
Discrete univariate random variate generation
WSC '83: Proceedings of the 15th conference on Winter simulation - Volume 1Most of the early research done in random variate generation is in the area of continuous distributions. Not until 1979 was research published on exact, uniformly fast discrete univariate random variate generation. Since then the state of the art of ...
Random variate generation and connected computational issues for the Poisson---Tweedie distribution
After providing a systematic outline of the stochastic genesis of the Poisson---Tweedie distribution, some computational issues are considered. More specifically, we introduce a closed form for the probability function, as well as its corresponding ...
Efficient matrix-exponential random variate generation using a numeric linear combination approach
DEVS '14: Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS IntegrativeMatrix 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