Bayesian Estimation from Exponentiated Frechet Model using MCMC Approach based on Progressive Type-II Censoring Data

Based on progressively Type-II censored samples, the maxim um likelihood (ML) and Bayes estimators for the parameters as well as some lifetime parameters (reliability and hazard functions) of the exponentiated Frchet (EF) distribution a re derived. The confidence interval of the parameters are obtained based on a n asymptotic distribution of maximum likelihood estimator s. Further; we consider delta method and bootstrap method to construct app roximate confidence intervals for reliability and hazard fu nctions. The Bayes estimators of the unknown parameters cannot be obtain ed in closed form. Markov chain Monte Carlo (MCMC) method has been used to compute the approximate Bayes estimates and also to c onstruct the highest posterior density (HPD) credible inte rvals. The results of Bayes estimators are obtained under both the bala nced squared error loss (BSEL) and balanced linear-exponen tial (BLINEX) loss. A practical example consisting of data represents a re lief time of arthritic patients reported by Wu et al. [ 1] was used for illustration, Finally; some numerical results using simulation study con cer ing different sample sizes and different progressive c ensoring schemes were reported.