Abstract
A new algorithm for sampling from beta(p, q) distributions with parametersp>1,q>1 is developed. It is based on a method by Minh [9] which improves acceptance-rejection sampling in the main part of the distributions. Additionally, transformed uniform deviates can often be accepted immediately, so that much fewer than two uniforms are needed for one beta variate, on the average. The remaining tests for acceptance are enhanced by ‘squeezes’. Experiments covering a wide range of pairs (p, q) showed improvements in speed over competing algorithms in most cases.
Zusammenfassung
Ein neuer Algorithmus zur Erzeugung von Stichproben aus Beta(p, q)-Verteilungen mit Parameternp>1,q>1 wird entwickelt. Er basiert auf einer Methode von Minh [9], welche die Verwerfungstechnik im Hauptteil der Verteilungen verbessert. Zusätzlich können transformierte gleichverteilte Zufallszahlen oft sofort akzeptiert werden, so daß im Durchschnitt viel weniger als zwei gleichverteilte Zufallszahlen pro Beta-Stichprobe benötigt werden. Die verbleibenden Annahmetests werden durch “Squeezes” verbessert. Versuche über einen weiten (p, q)-Bereich ergaben in den meisten Fällen Geschwindigkeitssteigerungen im Vergleich zu konkurrierenden Methoden.
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References
Ahrens, J. H., Dieter, U.: Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing12, 223–246 (1974).
Atkinson, A. C.: A family of switching algorithms for the computer generation of beta random variables. Biometrika66, 141–145 (1979).
Atkinson, A. C., Whittaker, J.: A switching algorithm for the generation of beta random variables with at least one parameter less than 1. J. Roy. Statist. Soc. A139, 462–467 (1976).
Atkinson, A. C., Whittaker, J.: Algorithm AS 134: The generation of beta random variables with one parameter greater than one and one parameter less than 1. Applied Statistics28, 90–93 (1979).
Cheng, R. C. H.: Generating beta variates with nonintegral shape parameters. Comm. ACM21, 317–322 (1978).
Devroye, L.: Non-uniform random variate generation. Berlin, Heidelberg, New York: Springer 1986.
Dieter, U., Ahrens, J. H.: Acceptance-rejection techniques for sampling from the gamma and beta distributions. Techn. Report83, Dep. Statist., Stanford Univ., Stanford, California 1974.
Jöhnk, M. D.: Erzeugung von betaverteilten und gammaverteilten Zufallszahlen. Metrika8, 5–15 (1964).
Minh, Do Le: Generating gamma variates. ACM Trans. on Math. Software14, 261–266 (1988).
Sakasegawa, H.: Stratified rejection and squeeze method for generating beta random numbers. Ann. Inst. Statist. Math.35, 291–302 (1983).
Schmeiser, B. W., Babu, A. J. G.: Beta variate generation via exponential majorizing functions. Oper. Research28, 917–926 (1980). (Errata: Oper. Research,31, 802, 1983).
Stadlober, E., Kremer, R.: Sampling from discrete and continuous distributions with C-rand. In: Pflug, G., Dieter, U. (eds.) Simulation and Optimization, pp. 154–162, 1992 (Springer Lecture Notes Econom. Math. Systems371).
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Dedicated to Professor Ulrich Dieter on the occasion of his 60th birthday
This research was supported by the Austrian Research Council (Fonds zur Förderung der wissenschaftlichen Forschung Nr. P8257-PHY).
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Zechner, H., Stadlober, E. Generating beta variates via patchwork rejection. Computing 50, 1–18 (1993). https://doi.org/10.1007/BF02280036
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DOI: https://doi.org/10.1007/BF02280036