In this paper we investigate two classes of exponential dispersion models (EDMs) for overdispersed count data with respect to the Poisson distribution. The first is a class of Poisson mixture with positive Tweedie mixing distributions. As an approximation (in terms of unit variance function) of the first, the second is a new class of EDMs characterized by their unit variance functions of the form μ + μp, where p is a real index related to a precise model. These two classes provide some alternatives to the negative binomial distribution (p = 2) 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 the practical usefulness is also discussed.
@article{urn:eudml:doc:40459,
title = {Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Dem\'etrio classes.},
journal = {SORT},
volume = {28},
year = {2004},
pages = {201-214},
mrnumber = {MR2116192},
zbl = {1274.62122},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40459}
}
Kokonendji, Célestin C.; Dossou-Gbété, Simplice; Demétrio, Clarice G. B. Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes.. SORT, Tome 28 (2004) pp. 201-214. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40459/