Bayesian estimation of Marshall Olkin extended inverse Weibull under progressive type II censoring

The estimations of parameters and percentiles for a three‐parameter Marshall Olkin extended inverse Weibull distribution based on progressively type‐II censored sample are concerned. The Bayesian, least‐squares, maximum likelihood and percentiles estimate methods for the model parameters have been developed. Comparing all estimate methods, the least‐squares, maximum likelihood and percentiles estimate methods are shown not stable due to the identification problem in the extended parametric space. Therefore, the Bayes estimate methods are focused. Three Bayesian estimations of the distribution parameters and p percentiles for p=$p =$ 2.5, 50 and 97.5 under the squared error loss, absolute error loss and LINEX loss functions are respectively calculated by using the Markov chain Monte Carlo sampling procedure. Moreover, two real data sets are presented for the application illustration. Finally, concluding remarks are addressed.