Credibility Based on Accuracy

This paper shows that the optimal credibility split between two estimators is related to how well each estimator predicts the underlying experience. First, an equation is shown which expresses the credibility assigned to each estimator in terms of the average prediction error of the other estimator and the average squared difference between the two estimators. That equation is verified using the classic Bayesian credibility n/(n + k) formula and a formula for weighting prior observations of time series that was developed by the author. An enhancement to the classic Bayesian method for class credibilities is shown. Finally, the author shows that optimal credibility is proportional to the accuracy of each estimator, less the extent to which both estimators make the same errors. Keyword: Credibility