A Compound of Generalized Negative Binomial and Shanker Distribution

The objective of this paper is to provide an alternative distribution to the varieties of discrete distributions to be used to fit count data. We propose a compound of Generalized Negative Binomial and Shanker distribution, namely, the Generalized Negative Binomial-Shanker (GNB-SH) distribution. GNB-SH distribution can be used to fit count data while still maintaining similar characteristics as the traditional negative binomial. This new formulation is a generalization of new mixture distributions namely the Negative Binomial- Shanker (NB-SH) distribution and the Binomial-Shanker (BI-SH) distribution. Some mathematical properties of this distribution and that of its special cases are studied. Parameter estimation for GNB-SH and NB-SH distributions is also implemented using maximum likelihood.