On the generalization and estimation for the double Poisson distribution

Abstract

The bivariate forms of many important discrete probability distributions have been studied by many statisticians. The trinomial, the double Poisson, the bivariate negative binomial, and the bivariate logarithmic series distributions are in fact the bivariate generalizations of the well known univariate distributions. A systematic account of various families of distributions of bivariate discrete random variables have been given by Patil and Joshi (11), Johnson and Kotz (4), and Mardia (9) in their books. In this paper we introduce a new generalized form for the double Poisson distribution given by Joshi (5), and we discuss some of its interesting properties and application