A Bayes Study on the Feasibility of Shape and Threshold Parameters Based on the Assumption of Exponential and Weibull Models

Abstract

Exponential and Weibull models are commonly used models with former being the special case of the latter. In their most general forms, the exponential model involves both threshold and scale parameters whereas the Weibull model involves threshold, scale and shape parameters. The article analyzes the two models in a Bayesian framework and examines the feasibility of generality versus particularity in the sense that it tests for the possibility of (not) having a threshold and/or a shape parameter in the data arising from exponential (Weibull) model. The results are illustrated based on both complete and censored datasets from the models.

Keywords:

• Censored data
• Deviance information criterion
• Exponential model
• Gibbs sampler
• Posterior predictive loss criterion
• Predictive simulation
• Shape parameter
• Threshold parameter
• Weibull model

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62N03
• 62N05

Acknowledgment

The authors would like to thank the Associate Editor, and the referees for their valuable comments and suggestions that improved the earlier version of the manuscript.