On a class of bivariate compounded Poisson distributions

A unified treatment is given for a family of bivariate discrete distributions with marginals and conditionals being convoluted Poisson distributions. Using generating functions a number of results are obtained for probabilities, cumulants and factorial cumulants. Conditional distributions are also examined. Five illustrative examples are presented in detail. Applications to accident data are indicated.Convoluted Poisson distributions Bivariate Short Probability generating function Conditional distributions Accident data