Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

Abstract

In this study, we are interested in investigating the performance of likelihood inference procedures for the 𝑝𝑡ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research.