A Note on Full Credibility for Estimating Claim Frequency

The conventional standards for full credibility are known to be inadequate. This inadequacy has been well treated in the Mayerson, et. al. paper’ and in the ensuing discussions, where the general problem of estimating pure premium was considered. However, in spite of this previous treatment, that old, familiar number, 1,082, still enjoys widespread patronage. If, instead of estimating pure premium, we ignore claim severity and estimate only claim frequency, 1,082 claims, with the precision in estimation which it promises, is an acceptable standard, providing we are sampling from a homogeneous risk population and accept the usual assumption of mutual independence among risks having Poisson claim processes. However, we know the insureds are not a homogeneous population. We must provide for a distribution of the Poisson parameter over the population, referred to as the structure function.” The structure function introduces additional variation into the claim process which reduces the precision of estimation promised by the conventional credibility standards.