Evaluation of Beta Generation Algorithms

In this article, we provide an overview of well-known beta algorithms. We first study a stochastic search procedure proposed by Kennedy (1988) that asymptotically generates a beta variate. The goal is to identify the optimal parameter setting so that Kennedy's algorithm can achieve the fastest speed of generation. For comparative purposes, we next evaluate the performance of some selected beta algorithms in terms of the following criteria: (i) validity of choice of shape parameters; (ii) computer generation time; (iii) initial set-up time; (iv) goodness of fit; and (v) amount of random number generation required. Based on the empirical study, we present three useful guidelines for choosing the best suited beta algorithm.

[1]  G. Forsythe.  Von Neumann''s comparison method for random sampling from the normal and other distributions. , 1972 .

[2]  B. Schmeiser,et al.  Acceptance/Rejection Methods for Beta Variate Generation , 1980 .

[3]  Samuel Kotz,et al.  Use of moments in deriving distributions, and some characterizations , 1989 .

[4]  Bruce W. Schmeiser,et al.  Beta Variate Generation via Exponential Majorizing Functions , 1980, Oper. Res..

[5]  D. P. Kennedy.  A note on stochastic search methods for global optimization , 1988, Advances in Applied Probability.

[6]  M. Jöhnk.  Erzeugung von betaverteilten und gammaverteilten Zufallszahlen , 1964 .

[7]  D. Farnsworth.  A First Course in Order Statistics , 1993 .

[8]  Russell C. H. Cheng.  Generating beta variates with nonintegral shape parameters , 1978, CACM.

[9]  A. C. Atkinson.  A family of switching algorithms for the computer generation of beta random variables , 1979 .

[10]  A. Atkinson,et al.  The Computer Generation of Beta, Gamma and Normal Random Variables , 1976 .

[11]  H. Sakasegawa,et al.  Stratified rejection and squeeze method for generating beta random numbers , 1983 .

[12]  Joachim H. Ahrens,et al.  Computer methods for sampling from gamma, beta, poisson and bionomial distributions , 1974, Computing.

[13]  Max Henrion,et al.  Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis , 1990 .

[14]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[15]  A. C. Atkinson,et al.  A Switching Algorithm for the Generation of Beta Random Variables with at Least One Parameter Less than 1 , 1976 .

[16]  A. Narayanan.  Computer generation of dirichlet random vectors , 1990 .

[17]  Richard J. Cleary.  Handbook of Beta Distribution and Its Applications , 2006 .

[18]  Ernst Stadlober,et al.  Generating beta variates via patchwork rejection , 2005, Computing.

[19]  B. Arnold,et al.  A first course in order statistics , 1994 .

[20]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .