ON A BIVARIATE KATZ’S DISTRIBUTION

Abstract

In this paper, we propose the bivariate distribution of the univariate Katz distribution [7] using the technique of the product of marginal distributions by a multiplicative factor. This method has been examined in [11] and used in [9] to construct a bivariate Poisson distribution. The obtained model is a good way to unify bivariate Poisson, bivariate binomial and bivariate negative binomial distributions and has interesting properties. Among others, the correlation coefficient of the obtained model can be either positive, negative, or null, and the necessary condition of zero correlation is a necessary and sufficient condition for independence. We used two methods to estimate the parameters: the method of moments and the maximum likelihood method. An application to concrete insurance data has been made. This data concerns natural events insurance in the USA and third-party liability automobile insurance in France [13].