Bayesian and Non-Bayesian Estimation of Extended Exponential Distribution under Type-I Progressive Hybrid Censoring

Theestimatingproblemsofthemodelparameters,reliabilityandhazardfunctionsofextendedexponentialdistributionwhen sample is available from Type-I progressive hybrid censoring scheme will be considered. The maximum likelihood estimation has been obtained for any function of the model parameters. Based on the normality property of the classical estimators, approximate confidence intervals for the unknown parameters and any function of them are constructed. Further, to construct the asymptotic confidence interval of the reliability and hazard rate function. Using independent gamma priors, the Bayes estimators of the unknown parameters are derived based on both the symmetric squared error and asymmetric LINEX loss functions. Since the Bayes estimators are obtained in a complex form therefore, Markov Chain Monte Carlo using Metropolis-Hastings algorithm has been used to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. To evaluate the performance of the proposed methods, a Monte Carlo simulation study is carried out. Finally, we consider medical data to illustrate the applicability of the methods covered in the paper. Keywords