On the Calculation of the Generalized Poisson Function

Drs. H. Bohman and F. Esscher have reported in a recent paper 1) an extensive research performed in Sweden on the different methods of calculation of the distribution function of the total amount of claims. In the present paper certain methods are discussed in so far as they are different from those presented in the above quoted paper. The consideration is restricted to the generalized Poisson function even though some results can be easily extended. The author has already commented on some of the results represented in the sequel at a special meeting of the I7th International Congress of Actuaries in Edinburgh.