Shmueli et al. (2005) revived a useful discrete distribution called CMP (the Conway–Maxwell–Poisson distribution) 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.
CMP has been used in marketing applications (Boatwright et al. 2003; Borle et al. 2005), and disclosure limitation (Kadane et al. 2006).
Recently, Sellers & Shmueli (2008) developed a CMP Regression model using a GLM approach. It includes Poisson regression and logistic regression as special cases.
See relevant publications.