The Mixed Bivariate Hoffmann Distribution

In this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case. We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature. This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution.