E-Bayesian estimations of the reliability and its E-posterior risk under different loss functions

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.

Keywords:

• E-Bayesian estimation
• E-posterior risk
• Binomial distribution
• Reliability
• Loss function
• Monte Carlo simulation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62F10
• 62N05

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).

Additional information

Funding

This work was supported partly by Zhejiang Province Natural Science Foundation [No. LY18A010026].