A new class of parametric regression models for both underand overdispersed count data is proposed. These models are based on squared polynomial expansions around a Poisson baseline density. The approach is similar to that for continuous data using squared Hermite polynomials proposed by Gallant and Nychka and applied to ®nancial data by, among others, Gallant and Tauchen. The count models are ...

Recently, count regression models have been used to model over dispersed and zero-inflated response variable that is affected by one or more covariates. Generalized Poisson (GP) negative binomial (NB) suggested deal with over-dispersion. Zero inflated such as the (ZIP), (ZINB) generalized Pois son (ZIGP) handle data many zeros. The aim of this study number C. caretta hatchlings dying from expos...

In their fundamental paper on cubic variance functions (VFs), Letac and Mora ( The Annals of Statistics , 1990) presented a systematic, rigorous comprehensive study natural exponential families (NEFs) the real line, characterization through VFs mean value parameterization. They section that for some reason has been left unnoticed. This deals with construction associated NEFs counting distributi...