Bayes Analysis of a Three-Parameter Pareto Distribution via Sample Based Approaches

SYNOPTIC ABSTRACT

This paper considers an important but less explored model, namely the three-parameter Pareto distribution that, besides having applications in many important areas, has been advocated in the context of failure time data analysis. The analysis has been done using both the Gibbs sampler vs. the Metropolis algorithm, and it has been shown that the Metropolis algorithm offers significant improvement over the Gibbs sampler. The extension of the two algorithms for censored situations is also given. For numerical illustration, we have considered both the real and the simulated data sets from the model. In the second part of the study, we illustrate the assumed model on the basis of a real data set using the tool kits of Bayesian predictive simulation ideas.

Key words:

• failure time
• Markov chain Monte Carlo procedure
• Gibbs sampler
• Metropolis algorithm
• Bayesian predictive simulation
• censored data