A portfolio of 200 insurance policies for which the claim counts are Poisson- distributed produces an overall average of 0.625 claims per policy per year. This portfolio consists of 4 disjoint subportfolios, where the claim count dis- tribution in the rst subportfolio is Poisson with mean 0.15, the claim count distribution in the second subportfolio is Poisson with mean 0.45, the claim count distribution in the third subportfolio is Poisson with mean 0.90 and the claim count distribution in the fourth subportfolio is Poisson with mean 1.45. Also, the number of policies in the rst subportfolio is 40, in the second one is 80, in the third one is 60 and in the fourth one is 20.