Bayesian Inference for the Generalized Exponential Distribution Based on Progressively Censored Data

Abstract

Based on a progressively Type-II censored sample, Bayesian estimation of the parameters as well as Bayesian prediction of the unobserved failure times from the generalized exponential (GE) distribution are studied. Importance sampling is used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are considered for predicting times to failure of units in multiple stages. A numerical simulation study involving three data sets is presented to illustrate the methods of estimation and prediction.

Keywords:

• Bayesian estimation
• Bayesian prediction
• Generalized exponential distribution
• Gibbs and Metropolis sampling
• Importance sampling
• Maximum likelihood estimation

Mathematics Subject Classification:

• 62F10
• 62F15
• 62F25
• 62E25

Acknowledgments

The authors would like to thank the two referees for their thorough review of the article and their valuable suggestions that improved on the original version of the manuscript.