Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring

In this paper, objective Bayesian analysis of Pareto distributions under progressive Type-II censoring is considered. Three types of noninformative priors (Jeffreys prior, two reference priors and two general forms of second order probability matching prior) are given. We show that one of the reference priors is also the second order probability matching prior (PMP). However, this reference prior, as well as the Jeffreys prior and PMPs, are related to the censoring scheme of life tests. Thus the other reference prior is preferred, and the proprieties of the posterior are discussed based on it. The simulation shows that the second reference prior leads to the required frequentist property. A real data from Crowley and Hu (1977) is analyzed for the purpose of illustration.