Bayesian and maximum likelihood estimations from parameters of McDonald Extended Weibull model based on progressive type-II censoring

In recent years, there have been many efforts to develop a new statistical distribution with more flexibility that can be fitted well to complex data. In this article we consider the statistical inference of the six-parameter McDonald extended Weibull distribution (McEW) based on the progressively Type-II censored sample. The maximum likelihood estimates (MLEs) of the six parameters and their asymptotic distribution are obtained. Based on the asymptotic distribution, the asymptotic confidence limits of its parameters can be computed. We also propose bootstrap confidence intervals of the parameters. The Bayes estimates and the associated highest posterior density credible intervals are computed using the Markov-chain Monte Carlo (MCMC) method, including the Gibbs sampling technique and Metropolis-Hastings algorithm. Simulation experiments are performed to compare the proposed methods and the corresponding confidence intervals under the different censoring schemes. Finally, concluding remarks are given.