Based on progressively Type-II censored samples, the maximum likelihood (ML) and Bayes estimators for the parameters as well as some lifetime parameters (reliability and hazard functions) of the exponentiated Frchet (EF) distribution are derived. The confidence interval of the parameters are obtained based on an asymptotic distribution of maximum likelihood estimators. Further; we consider delta method and bootstrap method to construct approximate confidence intervals for reliability and hazard functions. The Bayes estimators of the unknown parameters cannot be obtained in closed form. Markov chain Monte Carlo (MCMC) method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density (HPD) credible intervals. The results of Bayes estimators are obtained under both the balanced squared error loss (BSEL) and balanced linear-exponential (BLINEX) loss. A practical example consisting of data represents a relief time of arthritic patients reported byWu et al.  was used for illustration, Finally; some numerical results using simulation study concerning different sample sizes and different progressive censoring schemes were reported.
A. Soliman, Ahmed; H. Abd Ellah, A.; A. Ahmed, Essam.; and A. Farghal, Al-Wageh
"Bayesian Estimation from Exponentiated Frechet Model using MCMC Approach based on Progressive Type-II Censoring Data,"
Journal of Statistics Applications & Probability: Vol. 4
, Article 6.
Available at: https://dc.naturalspublishing.com/jsap/vol4/iss3/6