A new over-dispersed count model

TL;DR

This paper introduces the PoiG distribution, a new two-parameter count model derived from Poisson and geometric distributions, useful for modeling over-dispersed count data with detailed statistical properties.

Contribution

The paper proposes the PoiG distribution, a novel over-dispersed count model, and explores its properties, estimation methods, and potential applications.

Findings

Derivation of the PoiG distribution from Poisson and geometric distributions

Analysis of statistical properties including generating functions and moments

Estimation methods like method of moments and maximum likelihood

Abstract

A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and geometric distributions and can be used for modelling over-dispersed as well as equi-dispersed count data. A number of important statistical properties of the proposed count model, such as the probability generating function, the moment generating function, the moments, the survival function and the hazard rate function. Monotonic properties are studied, such as the log concavity and the stochastic ordering are also investigated in detail. Method of moment and the maximum likelihood estimators of the parameters of the proposed model are presented. It is envisaged that the proposed distribution may prove to be useful for the practitioners for modelling over-dispersed count data compared to its closest competitors.