Abstract
We present a short algorithm for generating random variates with log-concave densityf onR and known mode in average number of operations independent off. Included in this class are the normal, gamma, Weibull, beta and exponential power (all with shape parameters at least 1), logistic, hyperbolic secant and extreme value distributions. The algorithm merely requires the presence of a uniform [0, 1] random number generator and a subprogram for computingf. It can be implemented in about 10 lines of FORTRAN code.
Zusammenfassung
Wir legen einen kurzen Algorithmus zur Erzeugung von Zufallsveränderlichen mit log-konkaver Dichtef aufR mit bekanntem Median-Wert vor. Die mittlere Anzahl der erforderlichen Operationen ist unabhängig vonf. Die log-konkaven Dichtefunktionen beschreiben u. a. die Normal-, Gamma-, Weibull-, Beta-, Potenzexponential- (alle mit Formparameter mindestens 1), Perks- und Extremwert-Verteilung.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Tables. New York: Dover Publications 1970.
Ahrens, J. H., Dieter, U.: Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing12, 223–246 (1974).
Best, J. D.: Letter to the editor. Applied Statistics27, 181 (1978).
Cheng, R. C. H.: The generation of gamma variables with non-integral shape parameter. Annals of Statistics26, 71–75 (1977).
Davidovic, Ju. S., Korenbljum, B. I., Hacet, B. I.: A property of logarithmically concave functions. Dokl. Akad. Nauk SSR185, 477–480 (1969).
Devroye, L.: On the computer generation of random variates with monotone or unimodal densities. Computing32, 43–68 (1984).
Gumbel, E. J.: Statistics of Extremes. New York: Columbia University Press 1958.
Ibragimov, I. A.: On the composition of unimodal distributions. Theory of Probability and Its Applications1, 255–260 (1956).
Jorgensen, B.: Statistical Properties of the Generalized Inverse Gaussian Distribution (Lecture Notes in Statistics, Vol. 9). Berlin-Heidelberg-New York: Springer 1982.
Lekkerkerker, C. G.: A property of log-concave functions I, II. Indagationes Mathematicae15, 505–521 (1953).
Perks, W. F.: On some experiments in the graduation of mortality statistics. Journal of the Institute of Actuaries58, 12–57 (1932).
Prekopa, A.: On logarithmic concave measures and functions. Acta Scientiarium Mathematicarum Hungarica34, 335–343 (1973).
Tadikamalla, P. R., Johnson, M. E.: A complete guide to gamma variate generation. American Journal of Mathematical and Management Sciences1, 213–236 (1981).
Talacko, J.: Perks' distributions and their role in the theory of Wiener's stochastic variables. Trabajos de Estadistica7, 159–174 (1956).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Devroye, L. A simple algorithm for generating random variates with a log-concave density. Computing 33, 247–257 (1984). https://doi.org/10.1007/BF02242271
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02242271