Choice Between Weibull and Lognormal Models: A Simulation Based Bayesian Study

Abstract

The Weibull and the lognormal distributions are the most widely used models for analyzing a variety of data from different fields. It is often seen that the two models quite nicely represent a given data set although the concerned analyses and the related inferential procedures may differ drastically. It is, therefore, highly desirable to study the behavior of the two models for a given set of observations in the light of recent tool-kits of model comparison/model choice. The article considers examining the issue of choosing the right model through a simulation based Bayesian study using the output from the Gibbs sampler.

Keywords:

• Weibull distribution
• Lognormal distribution
• Threshold parameter
• Gibbs sampler
• Predictive simulation
• Posterior predictive p-value
• Posterior Bayes factor
• Fractional Bayes factor
• Non-informative prior
• Posterior and predictive inferences