Experience Rating and Credibility

Abstract

Classical statistics deals with the following standard problem of estimation:Given: random variables X1, X2 … Xn independent, identically distributed, andobservations x1, X2 … xn,Estimate: parameter (or function thereof) of the distribution function common to all Xi.It is not surprising that the “classical actuary” has mostly been involved in solving the actuarial equivalent of this problem in insurance, namelyGiven: risks R1R2 … Rn no contagion, homogeneous group,Find: the proper (common) rate for all risks in the given class.There have, of course, always been actuaries who have questioned the assumptions of independence (no contagion) and/or identical distribution (homogeneity). As long as ratemaking is considered equivalent to the determination of the mean, there seem to be no additional difficulties if the hypothesis of independence is dropped. But is there a way to drop the condition of homogeneity (identical distribution)?