On certain properties of a class of bivariate compound poisson distributions and an application to earthquake data

The univariate compound Poisson distribution has many applications in various areas such as biology, seismology, risk theory, forestry, health science, etc. In this paper, a bivariate compound Poisson distribution is proposed and the joint probability function of this model is derived. Expressions for the product moments, cumulants, covariance and correlation coefficient are also obtained. Then, an algorithm is prepared in Maple to obtain the probabilities quickly and an empirical comparison of the proposed probability function is given. Bivariate versions of the Neyman type A, Neyman type B, geometric-Poisson, Thomas distributions are introduced and the usefulness of these distributions is illustrated in the analysis of earthquake data.