Smoothing Variate Generation

Abstract

Generating discrete variates in their own right is a discontinuous process. Nevertheless, we generate them so that they are used “smoothly” — in a sense we make precise. To do this, we use a procedure somewhat analogous to our smoothing of discrete summmation in Section 7.1. Though it is not practical to use this method in wholesale fashion to generate many discrete variates in a single simulation run, it is practical when applied only to a few variates per run and those variates are the first generated — as in the Poisson case (where we generally apply it only to the Poisson variable, with a possible exception in Example 8.2.1). We show below that our procedure produces unbiased output.