On the Estimation of Generalized Lifetime Performance Index Based on Exponentiated Exponential Distributed Characteristics Under Progressive Censoring

In this article, the generalized lifetime performance index (GLPI) is taken into consideration where the process distribution follows exponentiated exponential distribution. The different classical estimation procedures, namely, maximum likelihood estimation (MLE), least squares, weighted least squares, and maximum product spacing estimation (MPSE) methods have been discussed using progressively type-II censored samples. Next, the Bayesian estimation of the considered index with gamma prior distribution has been derived using the symmetric as well as asymmetric loss functions. Further, the different parametric interval estimation techniques, namely, asymptotic confidence interval based on MLE and MPSE, bootstrap confidence intervals, and Bayes credible intervals have been obtained for the considered censoring schemes. Monte Carlo simulation study has been carried out to compare these estimators in terms of their mean squared errors and simulated posterior risks, respectively. Lastly, two real data sets have been re-analyzed to illustrate applications of the proposed GLPI under progressively type-II censored scheme.