Table methods for random variate generation

Abstract

For stochastic simulation, the generation of random variates from different distributions is a prerequisite. In certain programming languages and software, there are already random variate generation functions of standard distributions. However, for generating random variates from non-standard distributions or quasi-densities, we need universal algorithms. In this research, we come up with two universal random variate generation methods, namely the Triangular Ahrens and the Polynomial Density Inversion. We try to see if they are competitive with existing methods with respect to simplicity, speed and other performance criteria. After explaining the basics of the algorithms, we define the pseudo-codes in detail. Both of the algorithms are coded in C in a comprehensible and elegant way. Numerical results indicate that both of the algorithms execute with a successful performance. The Triangular Ahrens, which is a rejection method, has a smaller rejection constant while it requires smaller tables. The Polynomial Density Inversion, which approximates the density with piecewise polynomials, is more complicated however we obtain outstanding approximations with smaller tables. It also has a faster marginal execution time which makes the Polynomial Density Inversion a preferable method for a large number of random variates.