Useful moment and CDF formulations for the COM-Poisson distribution

摘要

The Poisson distribution is as important for discrete events as the normal distribution is to large sample data. In this note, we discuss a generalized Poisson distribution recently introduced in the statistics literature. We derive-for the first time-exact and explicit expressions for its moments and the cumulative distribution function for the case of over-dispersion. Computational issues are discussed to show the real value of these expressions.