Bayesian Estimation for Extension of Exponential Distribution Under Progressive Type-II Censored Data Using Markov Chain Monte Carlo Method

In this paper, we consider the classical and Bayesian estimation of the parameters, reliability function and hazard function for a new extension of exponential distribution under progressive Type-II censored data using asymmetric loss functions. In most of the cases, it has been observed that the Classical and Bayes estimator of the parameters do not appear in explicit form. Therefore, Newton- Raphson (N-R) and Markov Chain Monte Carlo (MCMC) methods have been used to obtain the classical as well as Bayes estimates respectively. Further, we have also constructed the 95% asymptotic confidence interval based on maximum likelihood estimates (MLEs) and highest posterior density (HPD) credible intervals based on MCMC samples. A Monte Carlo simulation study is carried out to compare the performance of Bayes estimators with the corresponding classical estimators in terms of their simulated risk (average loss over whole sample space