An example of credibility and shifting risk parameters

Abstract

In this paper. the won-lost record of baseball teams will be used to examine and illustrate credibility concepts. This illustrative example is analogous to the use of experience rating in insurance. It provides supplementary reading material for students who are studying credibility theory. This example illustrates a situation where the phenomenon of shifring parameters over time has a very significant impact. The effects of this phenomenon are examined. Three different criteria that can be used to select the #primal credibility are examined: least squares, limited jluctuation and MeyersJDorweiler. In applications, one or more of these three criteria should be useful. it is shown that the mean squared error can be written as a second order polynomial in the credibilities with the coefjicients of this polynomial written in terms of the covariance structure of the data. It is then shown that linear equation(s) can be solved for the least squares credibiliries in terms of the covariance structure. The author wishes to thank Julie Jannuzzi and Gina Brewer for typing this paper