A note on a universal random variate generator for integer-valued random variables

TL;DR

This paper introduces a universal rejection-based generator for integer-valued, square-integrable random variables, capable of efficiently generating classical and complex distributions with closed-form characteristic functions.

Contribution

It presents a simple, implementable algorithm that extends existing methods to a broader class of integer-valued distributions, including those without explicit probability functions.

Findings

Effective for classical distributions like Poisson and Binomial

Suitable for distributions with closed-form characteristic functions

Demonstrated with Poisson-Tweedie distribution example

Abstract

A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal gives rise to a simple algorithm which may be implemented in a few code lines and which may show good performance when the classical families of distributions - such as the Poisson and the Binomial - are considered. In addition, the method is suitable for the computer generation of integer-valued random variables which display closed-form characteristic functions, but do not possess a probability function expressible in a simple analytical way. As an example of such a framework, an application to the Poisson-Tweedie distribution is provided.