Auto insurance claims come from policies that are classified into three groups, corresponding to different deductible amounts and the expected size of an eventual claim. The classifications are: Low (L), Medium (M) and High (H). Historically, 80% of all claims are classified L, 15% are classified M and the remaining are classified H. In addition to the large expected differences in observed in claim sizes between each of these three groups, differences are also expected to be observed in claim amounts within each classification group. To reflect this, claims within each group are described as arising from a shifted Pareto probability distribution, with the random claim amounts having probability density function (pdf) given by 202 fy (y | 0 ; ) = 23 , y > Oj, for y in group j, and j = L, M and H and where where Y = y represents the size of an individual claim, in $1000 dollars. Note that if y _ 0;, then fy (y | 0;) is defined to equal zero. The parameter for each of the classes L, M and H, are given by OL = 1, 0M = 3 and OH = 7. Note that although there is a different lower bound on the size of a claim for each classification, there is no upper bound