Ӧ�ø���ͳ�� 2015, 31(3) 225-237 DOI:      ISSN: 1001-4268 CN: 31-1256

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The Empirical Bayes Estimation of Risk Parameters in Pareto Claim Distribution
Wen Limin, Zhang Mei, Cheng Zihong, Zhang Yi
School of Mathematics and Information Science, Jiangxi Normal University; School of Information Management, Jiangxi University of Finance and Economics; School of Computer and Information Engineering, Jiangxi Normal University

The Bayesian model is established in this paper, and the risk
parameters of claim amounts in Pareto distribution are estimated. The maximum likelihood
estimation, Bayesian estimation and credibility estimation are derived and the strong
consistency of these estimates are proved. We also compared their mean square error both
in theory and in numerical simulation. The results show that Bayesian estimation is better
than other estimates in sense of mean square error. Finally, the structural parameters in
Bayes estimation and credibility estimation are estimated and the corresponding empirical
Bayes estimates are proved asymptotically optimal.

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