The COM‐Poisson model for count data: a survey of methods and applications

Abstract

The Poisson distribution is a popular distribution for modeling count data, yet it is constrained by its equidispersion assumption, making it less than ideal for modeling real data that often exhibit over‐dispersion or under‐dispersion. The COM‐Poisson distribution is a two‐parameter generalization of the Poisson distribution that allows for a wide range of over‐dispersion and under‐dispersion. It not only generalizes the Poisson distribution but also contains the Bernoulli and geometric distributions as special cases. This distribution's flexibility and special properties have prompted a fast growth of methodological and applied research in various fields. This paper surveys the different COM‐Poisson models that have been published thus far and their applications in areas including marketing, transportation, and biology, among others. Copyright © 2011 John Wiley & Sons, Ltd.