The Credible Distribution.
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Credibility theory is concerned with the problem of forecasting the mean performance claim frequency, total losses, etc. of an individual risk, selected from a collective of heterogeneous risks, based upon the statistics of the collective, and upon the individuals experience data. The classic results, derived by American actuaries in the 1920s, were further strengthened by Bailey and Mayerson in 1950 and 1965, who showed that these results were exact Bayesian for certain risk distributions. Buhlmann, in 1967, then showed that the credibility formulae were the best least-squares linearized approximation to the exact Bayesian forecast, for general risk distributions. The paper extends credibility theory to the problem of forecasting the distribution of individual risk, based upon collective statistics and individual experience data. Modified author abstract
- Economics and Cost Analysis
- Operations Research