Statistics and Computing

, Volume 24, Issue 4, pp 589–596

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


DOI: 10.1007/s11222-013-9390-8

Cite this article as:
Barabesi, L. & Pratelli, L. Stat Comput (2014) 24: 589. doi:10.1007/s11222-013-9390-8


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.


Rejection methodInversion formulaPoisson-Tweedie distributionLuria-Delbrück distribution

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Economics and StatisticsUniversity of SienaSienaItaly
  2. 2.Accademia NavaleLivornoItaly