E-Bayesian estimation of reliability characteristics of two-parameter bathtub-shaped lifetime distribution with application

This article presents the expected Bayesian (E-Bayesian) estimation of the scale parameter, reliability and failure rate functions of two-parameter bathtub-shaped lifetime distribution under type-II censoring data with. Squared error loss function and gamma distribution as a conjugate prior distribution for the unknown parameter are used to obtain the E-Bayesian estimators. Also, three different prior distributions for the hyperparameters for the E-Bayesian estimators are considered. Some properties of the E-Bayesian estimators are studied. Using minimum mean square error criteria, a simulation study is conducted to compare the performance of the E-Bayesian estimators and the corresponding Bayes and maximum likelihood estimators. A real data set is analysed to show the applicability of the different proposed estimators. The numerical results show that the E-Bayesian estimators perform better than the classical and Bayesian estimators.