A New Distribution for Overdispersed Count Data

This work aims to introduce a novel distribution for count data which is capable of accounting for issues such as overdispersion and an excess of zeros. Currently, the reference distributions for handling such data are the negative binomial (NegBin) and the beta-negative binomial (BNB). The proposed distribution, named the flexible beta-negative binomial (FBNB), exhibits a compound structure that resembles that of the BNB while increasing flexibility in capturing heavy tails, excess of zeros, and latent structures in the data. The paper illustrates the characterization of the FBNB as a special finite mixture with two BNB components, shows the moments of the FBNB, and provides insights into the interpretation of its parameters. In addition, a brief introduction of a regression model aimed at evaluating the impact of covariates on the component-specific means is provided. It is worth noting that the results concerning the estimation of unknown parameters for both the FBNB and the associated regression model are still in the preliminary stages and, as such, are not presented in this paper.