A New Regression Model for Over-Dispersed Count Responses Based on Poisson and Geometric Convolution

This article presents an alternative generalized linear regression model specifically designed for count responses that exhibit over-dispersion. The recently developed PoiG distribution features a closed-form expression of the mean unlike many over-dispersed count data models such as the popular COM-Poisson (CMP) distribution. A reparametrized version of the PoiG distribution is proposed in the current work to demonstrate its flexible properties in modelling over-dispersed counts with covariates. The parameters of the proposed regression model are estimated using the method of maximum likelihood estimation and the respective confidence intervals are computed using bootstrap routine. Three benchmark real-world datasets are used to demonstrate the application of the proposed modelling approach. The proposed model is found to be more suitable for modelling over-dispersed count data compared to its closest competitors.