Abstract
In this paper, we invoke a new prospective to discuss the estimation of a three-parameter Marshall Olkin extended inverse Weibull distribution based on Markov Chain Monte Carlo (MCMC) approach. The Bayes estimators under the squared error loss and LINEX loss functions are derived for three parameters. MCMC approach is applied to compute the Bayesian estimation of the unknown parameters. Using a real data application, it is shown that the superior performance of Bayesian estimation.