Noninformative priors for the common shape parameters of Weibull distributions

The Weibull distribution is widely used in survival analysis, reliability engineering, and failure analysis. In this paper, we develop noninformative priors such as probability matching priors for the common shape parameter of Weibull models using the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. Here, various matching criteria, such as quantile matching, matching of distribution function, highest posterior density matching, and matching via inversion of test statistics, are considered. Next, we derive the reference priors for groups of ordering. It also shows that most reference priors do not satisfy the first order matching criterion, but the one-at-a-time reference prior is the second order matching priors. A simulation study is performed and a real example is given.