A Note on the Use of Statistics in Rate Determination

Errors in the use and interpretation of the techniques developed in mathematical statistics can lead to false conclusions that are hazardous when used for decision making purposes. One primary danger is that of understating the probability of a catastrophic event. Below is presented an example in which a slight misuse of statistics has led to an erroneous statement concerning the reliability of a procedure for constructing an insurance premium. A very interesting recent article' in this Journal presented an example to determine the premium to be charged to an insured such that the insurer could be confident that the average loss for his policyholders would (in the long run) not exceed the premium more than once in one hundred periods. Let us begin by abstracting the problem from its context and then apply the proper statistical techniques to obtain the desired solution. Finally, the solution will be given its proper interpretation back in the context of the problem. Consider the set of possible consumers for a given policy. This population is conditioned by (a) the underwriting for the policy and (b) the individuals who have a desire to purchase this particular