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Credibility theory is a branch of actuarial mathematics concerned with determining risk premiums. It is employed to combine multiple estimates into a summary estimate that takes into account information on the accuracy of the initial estimates. For example, in group health insurance an insurer is interested in calculating the risk premium, , (i.e. the theoretical expected claims amount) for a particular employer in the coming year. The insurer will likely have an estimate of historical overall claims experience, , as well as a more specific estimate for the employer in question, . Assigning a credibility factor, , to the overall claims experience (and the reciprocal to employer experience) allows the insurer to get a more accurate estimate of the risk premium in the following manner:
The credibility factor is derived by calculating the maximum likelihood estimate which would minimise the error of estimate. Assuming the variance of and are known quantities taking on the values and respectively, it can be shown that should be equal to: Therefore, the more uncertainty the estimate has, the lower is its credibility.