Bayesian Inference in Dependent Right Censoring

Abstract

In this article, we consider dependent right censoring when the lifetime and censoring variables have a Marshall–Olkin bivariate exponential distribution and obtain MLEs, MMEs and UMVUEs of the unknown parameters. The Bayes estimators as well as the Posterior Regret Gamma Minimax (PRGM) estimators of the parameters of interest under the SEL function are also obtained and a Monte Carlo simulation study is carried out to compare these estimators.

Keywords:

• Bayes estimation
• Dependent right censoring
• Lifetime data
• Marshall–Olkin bivariate exponential distribution
• Posterior regret Gamma minimax estimation
• Robust Bayes

Mathematics Subject Classification:

• Primary 62N01, 62N02, 62C10
• Secondary 62F10, 62F15, 62F35, 62F40

Acknowledgment

The authors are grateful to the Editor, the referees, and Professor Mahbanoo Tata for making many helpful comments and suggestions. The second author's research was supported by a grant of the Research Council of the University of Tehran.

Notes

∗In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

∗In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

∗In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

∗In each box the first row presents the estimated MSE of the estimate and second row the corresponding bias is reported within parentheses.

∗The entries in the first and second rows of each box are, respectively, the estimated MSE of the estimate and the corresponding bias and, for the MCMC boxes, the third row shows the relevant estimate of τ.

∗The entries in the first and second rows of each box are, respectively, the estimated MSE of the estimate and the corresponding bias and, for the MCMC boxes, the third row shows the relevant estimate of τ.