Numerical Approach for Generating Beta Random Variates

Abstract

There are a number of probability density functions available to model time durations and other activities of interest in computer simulation programs. Among the available functions, the beta probability density function has been popular with practitioners of simulation because of its versatility, in that it can take on a variety a of shapes and easily fit sample distributions. The beta function also has specific upper and lower limits. This latter property is attractive since many applications do not require values at plus and minus infinity as would be modeled by the Gaussian, or normal, distribution. This paper describes a numerical technique for the generation of beta random variates where the beta parameters are not limited to integer values. By not limiting parameters to integer values, one must evaluate the beta normalizing constant as a gamma function rather than as a factorial function. A numerical technique for evaluating this gamma function by using a Gauss‐Laguerre approximation is discussed. An example problem using truck haul times is presented along with conclusions regarding the technique.