Statistical Inference on Progressive Type-II Censored Data from Extreme-value Distribution

We conduct statistical inference on data collected from extreme-value distribution under a progressive Type-II censoring scheme in this paper. By converting the extreme-value model into a Wei bull model, the computation of the maximum likelihood estimator (MLE) for model parameters can be greatly simplified. The bias, variance and covariance of the MLEs under various censoring schemes are investigated. Besides, based on the asymptotic normality of these MLEs, the coverage probability for some defined pivotal quantities and the average length of the confidence interval for model parameters are also provided. The properties of the derived censoring schemes are evaluated by a numerical study. The results show that in order to get satisfying performance in respect to bias, variance, coverage probability and average length of confidence intervals, a moderate or large number of failures are required. Furthermore, a sensitivity study is also employed to evaluate the robustness of our suggested approach, which shows that it is rather robust and the simulation results can be easily reproduced.