The Credible Distribution

Credibility theory is concerned with the problem of forecasting the mean performance (dana1 frequency, total losses, etc.) of an individual risk, selected from a collective of heterogeneous risks, based upon the statistics of the collective, and upon t h e individual's experience data. The classic results, derived by American actuaries in the i92o's, were further strengthened by Bailey and Mayerson in 195 ° and 1965, who showed t h a t 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.