Abstract
This paper presents a simple and easy to implement algorithm for sampling from the generalized four parameter gamma distribution proposed by Stacy. The proposed method is based on a generalization of Von Neumann's rejection method where the first stage sampling is done from the log logistic distribution. The proposed method is simple, easy to implement and faster than the traditional methods for generating generalized gamma variates.
Zusammenfassung
Es wird ein Algorithmus zur Erzeugung von Zufallszahlen, die nach der von Stacy vorgeschlagenen vierparametrigen verallgemeinerten Gammaverteilung verteilt sind, vorgestellt. Das vorgeschlagene Verfahren beruht auf einer Verallgemeinerung der Von Neumannschen Verwerfungsmethode, wobei die primären Zufallszahlen einer log-logistischen Verteilung entnommen werden. Die Methode ist einfach, leicht zu implementieren und schneller als die bisher bekannten Verfahren.
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References
Ahrens, J. H., Dieter, H.: Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing12, 223–246 (1974).
Atkinson, A. C.: An easily programmed algorithm for generating gamma random variables. Applied Statistics140, 232–234 (1977)
Atkinson, A. C., Pearce, M. C.: The computer generation of beta, gamma and normal random variables. Journal of Royal Statistical SocietyA 139, 431–461 (1976).
Cheng, R. C.: The generation of gamma variables with non-integral shape parameter. Applied Statistics26, 71–75 (1977).
Fishman, G. S.: Sampling from the gamma distribution on a computer. Communications of the ACM19, 407–409 (1975).
Greenwood, A. J.: A fast generator for gamma distributed random variables, in: CompStat (Bruckman, G., et al., eds.), pp. 19–27. Wien: Physica Verlag 1974.
Johnk, M. D.: Erzeugung von betaverteilten und gammaverteilten Zufallszahlen. Metrika8, 5–15 (1964).
Kinderman, A. J., Monahan, J. F.: Recent developments in computer generation of gamma and Student'st variables. A paper presented at the joint statistical meeting of ASA, Biometric Society, and IMS, Sandiego, Calif., 1978.
Lurie, D., Mason, R. L.: Empirical investigation of several techniques for computer generation of order statistics. Communications in Statistics2, 363–371 (1973).
Marsaglia, G.: A squeeze method for generating gamma random variables. Computers and Mathematics with Applications4, 231–236 (1977).
Stacy, E. W.: A generalization of the gamma distribution. Annals of Mathematical Statistics33, 1187–1192 (1962).
Tadikamalla, P. R.: Computer generation of gamma random variables. Communications of the ACM21, 419–422 (1978).
Tadikamalla, P. R.: Computer generation of gamma random variables—II. Communications of the ACM21, 925–928 (1978).
Tadikamalla, P. R., Johnson, M. E.: Some simple rejection methods for sampling from the normal distribution. Proceedings of the First International Conference on Mathematical Modeling, St. Louis, MO., pp. 573–578, 1977.
Tadikamalla, P. R., Johnson, M. E.: A survey of computer methods for sampling from the gamma distribution. Proceedings of the 1978 Winter Simulation Conference (forthcoming 1978).
Von Neumann, J.: Various techniques used in connection with random digits, Paper No. 13 in in “monte carlo method”. NBS Applied Mathematics Series No. 12, U. S. Government Printing Office, 1951.
Wallace, N. D.: Computer generation of gamma random variates with non-integral shape parameters. Communications of the ACM17, 691–695 (1974).
Whittekar, J.: Generating gamma and beta random variables with non-integral shape parameters. Applied Statistics23, 210–213 (1974).
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Tadikamalla, P.R. Random sampling from the generalized gamma distribution. Computing 23, 199–203 (1979). https://doi.org/10.1007/BF02252098
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DOI: https://doi.org/10.1007/BF02252098