On a Bivariate Katz's Distribution Constructed by the Trivariate Reduction Method

Abstract

In this paper, we propose the bivariate distribution of the Katz distribution [1] constructed by the trivariate reduction method, method developed in [6] and used in [5] to give an equivalent definition of the bivariate Poisson distribution [7, 8]. The constructed distribution includes, in particular, the bivariate Poisson distribution [5] and has interesting properties. For the estimation of the parameters, we used two methods: the method of moments and the maximum likelihood method using the EM algorithm. An application to concrete data has been made in order to carry out a comparative study between bivariate Poisson and Katz distributions, and we discuss the likelihood-ratio test, which assesses the goodness of fit of two competing statistical models.