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

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. This approach allows to create a dominating probability function, whose evaluation solely involves two integrals depending on the characteristic function of the random variable to be generated. 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, applications to the Poisson-Tweedie and the Luria-Delbrück distributions are provided.