Overdispersion and Poisson-Tweedie exponential dispersion models

Abstract. We investigate two sets of overdispersed models when Poisson distribution does not fit to count data: a class of Poisson mixture with Tweedie mixing distributions and a class of exponential dispersion models which have a unit variance function of the form µ + µp, where p is a real number. These two classes generalize the negative binomial distribution which is classically used in the framework of regression models for count data when overdispersion results in a lack of fit of the Poisson regression model. Some properties are then studied and discussed.