A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

Abstract

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Keywords:

• Fisher matrix
• Non informative priors
• Posterior distribution
• Reliability function
• Weibull distribution

Mathematics Subject Classification:

• Primary 62Fxx
• Secondary 62F15