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. 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.
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The authors would like to thank the two anonymous reviewers for their valuable comments and suggestions which have truly improved the early version of the paper.
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Barabesi, L., Pratelli, L. A note on a universal random variate generator for integer-valued random variables. Stat Comput 24, 589–596 (2014). https://doi.org/10.1007/s11222-013-9390-8
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DOI: https://doi.org/10.1007/s11222-013-9390-8