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.
Communications in Statistics - Simulation and Computation,38(4),750-770