Abstract
In this paper we propose the zero-modified Poisson-Sujatha distribution as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. It will be shown that the zero modification can be incorporated by using the zero-truncated Poisson-Sujatha distribution. A simple reparametrization of the probability function will allow us to represent the zero-modified Poisson-Sujatha distribution as a hurdle model. This trick leads to the fact that proposed model can be fitted without any previously information about the zero modification present in a given dataset. The maximum likelihood theory will be used for parameter estimation and asymptotic inference concerns. A simulation study will be conducted in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed model will be illustrated using real datasets of the biological sciences field and comparing it with other models available in the literature.
Highlights
Most applications involving the analysis of count data are performed using the Poisson and Negative Binomial distributions
The zero-modified PoissonSujatha (ZMPS) distribution expressed in a hurdle version contains the zero-truncated Poisson-Sujatha (ZTPS) distribution as one of its components, which differs from the traditional mixture representation of zero-inflated distributions
The ZMPS distribution was introduced as an alternative to model overdispersed count data having inflation or deflation of zeros
Summary
Most applications involving the analysis of count data are performed using the Poisson and Negative Binomial distributions. A relevant drawback of such compound models is the fact that they do not fit well when a large amount of zeros is observed To overcome this issue, several zero-inflated and hurdle approaches for standard Poisson model were proposed (Mullahy 1986; Lambert 1992; Zorn 1996). Shanker and Fesshaye (2016b) obtained the size-biased version of the Poisson-Sujatha distribution, presenting its properties and discussing its applications. Once zero inflated/deflated models may be useful to deal with data presenting overdispersion, this paper aims to introduce and present the usefulness of the zero modified version of the Poisson-Sujatha distribution, which is itself overdispersed.
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