Actuarial Science

Abstract

In the field of insurance mathematics it is important to specify the probability distribution for the cost of a single claim. From this specification one calculates the probability distribution for the total number of claims. According to Seal (1969) by far the greatest number of graduations of observed individual claim amounts have been based on the logmormal distribution, where it is assumed that the logarithm of the amount claimed follows the Gaussian law. The specification of a particular law for the cost of a single claim may not always be justifiable on axiomatic grounds, but nevertheless the tractability of the distribution is often a motivation behind its choice. Seal (1978) and Berg (1980) have advocated the use of the inverse Gaussian law in modelling claim cost distributions. In the following discussion we consider the approach taken by Berg to analyze loglinear claim cost analysis.