Percentiles Estimation for a Response Distribution

To estimate percentiles of a response distribution, the transformed response rule of Wetherill and Robbins-Monro sequential design were proposed under Log-Logistic model. Based on responses data, a necessary and sufficient condition for the existence of maximum likelihood estimators and then the calculating formula were presented. After a simulation study, the proposed approach was applied to 65# detonator. Numerical results showed that estimators of percentiles from the proposed approach are robust to the parametric models lacking information on the original response distribution.