A note on noninformative priors for Weibull distributions

Abstract

In this note, noninformative priors for two-parameter Weibull distributions are investigated. For one of the Weibull models, Berger and Bernardo's ( J. Amer. Statist. Assoc. 84 (1989), 200–207; In: Bayesian Statistics (1992), Oxford Univ. Press, Oxford, 35–60) forward and backward reference priors are shown to be the same, but differ from the Jeffreys prior. General forms of the second-order matching priors are derived, when one or both parameters are of interest. The Jeffreys prior is not a second-order matching prior, but the reference prior is a always a third-order matching prior. Furthermore, when both parameters are of interest, the reference prior is the unique second-order matching prior. Frequentist coverage probabilities of the small sample posterior confidence sets based on the Jeffreys and reference priors are compared. The reference prior is also superior to the Jeffreys prior for small sample sizes. It is also illustrated that the choice of a nuisance parameter is very important.