E-Bayesian estimation of the exponentiated distribution family parameter under LINEX loss function

ABSTRACT

This paper is concerned with using the E-Bayesian method for computing estimates of the exponentiated distribution family parameter. Based on the LINEX loss function, formulas of E-Bayesian estimation for unknown parameter are given, these estimates are derived based on a conjugate prior. Moreover, property of E-Bayesian estimation—the relationship between of E-Bayesian estimations under different prior distributions of the hyper parameters are also provided. A comparison between the new method and the corresponding maximum likelihood techniques is conducted using the Monte Carlo simulation. Finally, combined with the golfers income data practical problem are calculated, the results show that the proposed method is feasible and convenient for application.

KEYWORDS:

• E-Bayesian estimation
• exponentiated distribution family
• LINEX loss function
• Monte Carlo simulation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15

Acknowledgements

This work was supported partly by Ningbo Natural Science Foundation (No. 2013A610108). 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.