Exponential dispersion models for overdispersed zero-inflated count data

Abstract

We consider two classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. These classes were considered in our earlier paper as models of overdispersed zero-inflated distributions. In this paper we analyze the application of these classes to fit count data having overdispersed and zero-inflated statistics. For this reason, we first elaborate on the computational aspects of the probability distributions, before we consider the data fitting with our models. We execute an extensive comparison with other statistical models that are recently proposed, on both real data sets, and simulated data sets. Our findings are that our framework is a flexible tool that gives excellent results in a wide range of cases. Moreover, specifically when the data characteristics show also large skewness and kurtosis our models perform best.

Exponential Dispersion Models for Overdispersed Zero-Inflated Count Data

“…The remarks on the six worked out data fits describe typically our findings. We have executed an extensive numerical study on many more data sets, that were considered in literature, see our report Bar-Lev and Ridder (2020b) which is available on the arXiv. However, when we considered any study in the literature on fitting count data, we noticed that it applied the proposed model to just a few data sets, and then it gave good fits.…”