Count Data Model

Shmueli et al. (2005) revived a useful discrete distribution called the COM-Poisson (the Conway–Maxwell–Poisson) and introduced its statistical and probabilistic properties. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It is a member of the exponential family, and is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data.  Sellers & Shmueli (2010) developed a COM-Poisson Regression model using a GLM approach, which includes Poisson regression and logistic regression as special cases.    The distribution's flexibility and special properties has prompted a fast growth of methodological and applied research in various fields includeing marketing, online auctions, biology, transportation, and disclosure limitation, among others. A survey paper of the COM-Poisson by Sellers, Borle and Shmueli is forthcoming at ASMBI. See relevant publications.