Abstract
This paper studies the E-Bayesian estimations of the reliability and their E-posterior risk under different loss functions (including: squared error loss, weighted squared error loss, precautionary loss and K-loss) were derived under condition of binomial distribution. In the case of the one hyper parameter in order to measure the estimated risk, the definition of E-posterior risk (expected posterior risk)is proposed based on the definition of E-Bayesian estimation, and the formulas of E-Bayesian estimation and the formulas of E-posterior risk are developed, respectively. And an simulation example was given by using the Monte Carlo method. Finally, two practical problems were also performed to compare under different E-posterior risks (also using OpenBUGS). The results show that the proposed method is feasible and convenient for application.
Acknowledgments
The author wish to thank Professor Xizhi Wu, who checked the paper and gave author very helpful suggestions. The author are very grateful to the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).