Generalized Sichel Distribution and Associated Inference

Abstract

In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing the Poisson distribution with the extended generalized inverse Gaussian distribution. This distribution models over dispersed, zero-inflated and heavy-tailed count data sets. These characteristics are examined with respect to the dispersion, zero-inflation and the third central moment inflation indices. Examples are provided to compare the extension with several other existing models including the Poisson-inverse Gaussian and the Sichel distributions.

Keywords

• Poisson distribution; extended generalized inverse Gaussian distribution; overdispersion; zero-inflation; long-tailed distributions.