A generalized negative binomial distribution based on an extended Poisson process

Abstract

In this article we propose a generalized negative binomial distribution, which is constructed based on an extended Poisson process (a generalization of the homogeneous Poisson process). This distribution is intended to model discrete data with presence of zero-inflation and over-dispersion. For a dataset on animal abundance which presents over-dispersion and a high frequency of zeros, a comparison between our extended distribution and other common distributions used for modeling this kind of data is addressed, supporting the fitting of the proposed model.