Objective Bayesian analysis for Weibull distribution with application to random censorship model

Abstract

The article deals with an objective Bayesian analysis for Weibull distribution with application in random censorship model. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. We apply this method to random censorship model using Weibull distribution and compare it with Jeffreys and maximum likelihood methods. It is observed that the closed-form expressions for the Bayes estimators are not possible; we use importance sampling technique to obtain the approximate Bayes estimates. The behaviour of maximum likelihood and Bayes estimators is observed via extensive numerical simulation. The proposed methodology is used for the analysis of a real life application for illustration and appropriateness of the model is tested by Hollander and Proschan goodness-of-fit test specially designed for randomly censored data.