Random variate generation by fast numerical inversion in the varying parameter case
Christoph Baumgarten · Research in Statistics · 2023
There are various general techniques to produce random variates of a probability distribution such as the rejection method or numerical approaches to invert the cumulative distribution function (CDF). Some of these methods work in a black-box fashion (i.e., a single piece of code can sample for a relatively large class of distributions) which allows to create generators easily even for nonstandard distributions. Numerical inversion has some desirable properties that make its application appealing. However, a setup step is typically required to compute an approximation of the inverse of the CDF. Hence, if the distribution depends on a shape parameter and small samples are required for many different parameters (varying parameter case), the cost of the setup step typically outweighs the marginal generation times of the small samples, rendering the inversion method very slow. This article presents a new approach that allows for the use of inversion in the varying parameter case, provided that a suitable transformation of the density can be found to avoid running the setup for every parameter. The method is applied to two distributions (ARGUS and alpha distribution) to demonstrate that the performance is very good in the varying parameter case.