帕累托索赔分布中风险参数的经验贝叶斯估计

本文建立了贝叶斯模型,讨论了帕累托索赔额分布中参数的估计问题,得到了风险参数的极大似然估计、贝叶斯估计和信度估计,并证明了这些估计的强相合性.在均方误差的意义下比较了这些估计的好坏,并通过数值模拟对均方误差进行了验证,结果表明,贝叶斯估计比其他估计具有较小的均方误差.最后,给出了结构参数的估计并证明了经验贝叶斯估计和经验贝叶斯信度估计的渐近最优性.

The Empirical Bayes Estimation of Risk Parameters in Pareto Claim Distribution

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.