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

Authors:
Kimberly F. Sellers;Sharad Borle;Galit Shmueli
Affiliations:
Department of Mathematics and Statistics, Georgetown University, Washington, DC20057, USA;Department of Marketing, Jones Graduate School of Business, Rice University, Houston, TX77251, USA;Department of Decision, Operations and Information Technologies, Robert H. Smith School of Business, University of Maryland, College Park, MD20742, USA
Venue:
Applied Stochastic Models in Business and Industry
Year:
2012

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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.