The Optimal Number of Quantiles for Predictive Performance Testing of the NCCI Experience Rating Plan

Quantile testing is a key technique for fitting parameters and testing performance in workers compensation experience rating and the number of quantile intervals must be specified for such a test. A model is developed to compare the error in the quantile test empirical estimates of relative pure loss ratios to the interquantile differences between expected pure loss ratios. Theoretical model predictions are compared to empirical results from bootstrap quintile tests of the National Council on Compensation Insurance (NCCI) Experience Rating Plan (ERP). The model predicts that the noise-to-signal ratio grows in proportion to the 1.5 power of the number of quantiles and in inverse proportion to the 0.5 power of the sample size of risks. Empirical quintile and decile tests of NCCI’s Experience Rating Plan are consistent with model predictions. Increasing the number of quantiles requires a much greater proportional increase in data volume to maintain a constant noise- to-signal ratio. This explains the use of few quantiles, specifically quintiles, for testing NCCI’s Experience Rating Plan.