Graduation of Excess Ratio Distributions by the Method of Moments

A risk who wishes to be self-insured to a degree, and whose size as measured by expected losses is sufficient to make it practicable, may elect to have his premium based in part on actual losses up to a specified limit. The balance of his premium would consist of charges by the insurance carrier for claim service and other carrier expenses plus a charge for the expected or average value, based on the experience of many risks, of losses in excess of the specified limit.