Year: 1967
Type: article
Abstract: Classical statistics deals with the following standard problem of estimation: Given: random variables X1, X2 … Xn independent, identically distributed, and observations 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, namely Given: 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)?
Source: Astin Bulletin
Author: Hans Bühlmann
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2400614507