Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts?variation over and above that accounted for by the Poisson density. The extra-variation ? or dispersion ? is...

In this paper, we discuss discrete compound distributions, in which the counting distribution is a weighted Poisson distribution. The over- and under-dispersion of these distributions are then discussed by analyzing the Fisher index of dispersion as well as a newly introduced factorial moment to...

In this paper we consider spatial regression models for count data. We examine not only the Poisson distribution but also the generalized Poisson capable of modeling over-dispersion, the negative Binomial as well as the zero-inflated Poisson distribution which allows for excess zeros as possible...

Generalized linear models (GLM) are generalization of linear regression models, which allow fitting regression models to response data in all the sciences especially medical and dental sciences that follow a general exponential family. These are fl exible and widely used class of such models...

We discuss the modeling of count data whose empirical distribution is both multi-modal and over-dispersed, and propose the Hermite distribution with covariates introduced through the conditional mean. The model is readily estimated by maximum likelihood, and nests the Poisson model as a special...

Predictive modeling has been widely used for insurance rate making. In this paper, we focus on insurance claim count data and address their common issues with more flexible modeling techniques. In particular, we study the zero-inflated and hurdle-generalized Poisson and negative binomial...