The Poisson regression model is the most common framework for modeling count data, but it is constrained by its equidispersion assumption. The hyper-Poisson regression model described in this paper generalizes it and allows for over- and under-dispersion, although, unlike other models with the...

A biparametric discrete distribution that extends the Yule distribution is presented. It belongs to the family of distributions generated by the Gaussian hypergeometric function and it can be expressed as a generalized beta mixture of a geometric distribution. The introduction of a new parameter...

A regression model for count data based on the generalized Waring distribution is developed. This model allows the observed variability to be split into three components: randomness, internal differences between individuals and the presence of other external factors that have not been included...

The paper describes a distribution generated by the Gaussian hypergeometric function that may be seen as a generalization of the beta-binomial distribution. It is expressed as a generalized beta mixture of a binomial distribution. This new mixing distribution allows the existence of a mode and...