Estimation of Extreme Quantiles Based on Sensitivity Tests: A Comparative Study

Abstract

In reliability applications, it is often of interest to estimate extreme quantiles of the distribution of critical stimulus levels based on a limited number of sensitivity tests. To evaluate and compare the effectiveness of available sequential-design sensitivity tests in this setting, several such tests were compared through Monte Carlo simulation. Samples of size 20, 35, and 50 were used to estimate the .99 and, 999 quantiles of the probit model. Each test was evaluated using initial parameter estimates equal to the parameters of the model and then using inaccurate estimates. The effect of assuming the probit model when the true model was logit, generalized logistic, or Type I extreme-value was also studied. Our results show that, when the model is correctly specified, tests designed to estimate the model parameters and subsequently to estimate quantiles as a function of the model parameters provided more accurate quantile estimates than tests designed to estimate a specified quantile. The tests that estimated model parameters, however, were more affected by model misspecification.