Modeling Over-dispersion with two-Parameter Discrete Distributions

Abstract

In this paper we compare the performances of several two parameter discrete distributions in modeling over-dispersed count data. Particularly, we are interested in the performances of two newly proposed two parameter distributions, namely, the ATPPSD another two-parameter Poisson-Sujatha Distribution’ ATPPSD (Shanker et al., 2020) and the Bell-Tuchard (BT) distribution with some of other well known two-parameter discrete
distributions: the negative binomial (NB); the generalized Poisson (GP), the PoissonLindley (GPL), the discrete Weibull (DW) and the Poisson-inverse Gaussian (PIG) distributions. These distributions are applied to a variety of data sets exhibiting over dispersion. The two distributions perform poorly in most of the data set examples. Zero-inflated (ZI) versions of the models are also implemented because the regular models perform poorly with data exhibiting excess zeros.In most cases, the two distributions grossly underestimate the observed variances in the data sets and this subsequently lead to their poor fitting performances. The PIG and DW distributions will be suitable alternative models to the NB and GP models for modeling over dispersed count data.They perform in many cases better than the NB and GP models but the latter two models are very reliable and they both perform very well in most of the examples. For moderately over-dispersed data, the ATPPSD and BT distributions seem to do well.