ABSTRACT This paper studies the E-Bayesian estimations and their E-MSE of Pareto distribution parameter under different loss functions. In order to measure the estimated error, in the case of the two hyper parameters, the definition of E-MSE (expected mean square error) is introduced based on the definition of E-Bayesian estimation, and the formulas of E-Bayesian estimation and the formulas of E-MSE are given, respectively. Monte Carlo simulations are performed to analysis the performances of the proposed methods, results are compared on the basis of E-MSE. Finally, combined with the golfers income problem are performed to calculated, the maximum likelihood estimations of the shape parameter and scale parameter are given, respectively, and that compared and analysed with the E-Bayesian estimations; moreover, the Bayesian credible intervals of the shape parameter and scale parameter are also given, respectively, by MCMC method.

中文翻译：

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不同损失函数下Pareto分布参数的E-Bayesian估计及其E-MSE

摘要 本文研究了不同损失函数下Pareto分布参数的E-Bayesian估计及其E-MSE。为了度量估计误差，在两个超参数的情况下，在E-Bayesian估计的定义的基础上引入E-MSE（期望均方误差）的定义，E-Bayesian估计的公式和分别给出了 E-MSE 的公式。进行蒙特卡罗模拟以分析所提出方法的性能，并在E-MSE的基础上对结果进行比较。最后，结合高尔夫球员的收入问题进行计算，分别给出了形状参数和尺度参数的最大似然估计，并与E-Bayesian估计进行了比较和分析；而且，