Some Comments about the p-Generalized Negative Binomial (NBp) Model

This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., the NBp moment-generating function) with regard to the relationship between a sample mean and its accompanying variance, as well as spatial statistical/econometric numerical and empirical examples, whose parameter estimators are maximum likelihood or method of moment ones. Finally, it highlights the Moran eigenvector spatial filtering methodology within the context of generalized linear modeling, demonstrating it in terms of spatial negative binomial regression. Its overall conclusion is a bolstering of important findings the literature already reports with a newly recognized empirical example of an NB3 phenomenon.