Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data

In this paper, we investigate the problem of point and interval estimations for the modified Weibull distribution (MWD) using progressively type-II censored sample. The maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability and hazard functions). Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. Bayes estimates and the credible intervals are obtained under the assumptions of informative and noninformative priors. The results of Bayes method are obtained under both the balanced squared error loss (bSEL) and balanced linear-exponential (bLINEX) loss. We show that these loss functions are more general, which include the MLE and both symmetric and asymmetric Bayes estimates as special cases. Finally, Two real data sets have been analyzed for illustrative purposes.