A Class of Generalized Poisson and Mixture of Poisson and Generalized Poisson Distributions of order k

In this paper, aneffort is made to find out a class of GPDs of order k upon introducing a class of Quasi Binomial distribution of order k and using Abel’s generalization of theBinomial formula (Riordon, 1968, p. 18). A few particular cases, like a classof GPD, GPD of order k and classicalPoisson distribution have been studied. A mixture of Poisson and GeneralizedPoisson distribution along with their various inferential properties arediscussed. Finally, the mixture of Poisson and GP distributions are fitted tosome real life data and compared with classical Poisson distribution and GPDand the fittings of the mixture to the observed frequencies are found to bevery good as judged by the corresponding chi-square values.