Bivariate Poisson distribution

In the present thesis we deal with the bivariate Poisson distribution. A trivariate reduction method is used to define the bivariate Poisson dis- tribution. The theoretical characteristics of distribution, which this thesis deals with are the marginal distributions, covariance, a correlation coeffi- cient and the conditional distributions. A method of moments and a method of maximum likelihood are used to construct the point estimations of the parameters. Further, we focus on testing the goodness of fit by the index of dispersion test. A transforms of the sample correlation test is used to test the independence. Both methods for estimating the parameters and the statistic tests are applied to real data from the insurance field.