常见损失函数下逆伽马分布尺度参数的E-Bayes估计

E-Bayes Estimation of Scale Parameters of Inverse Gamma Distribution under Common Loss Functions

摘要: 为解决逆伽马分布参数的E-Bayes估计问题，本文对逆伽马分布在已知形状参数的情况下，讨论给出了尺度参数在平方损失函数与加权平方损失函数下的估计；同时基于Bayes估计，推导同条件下相应参数的E-Bayes估计，并运用蒙特卡洛方法进行随机模拟，验证E-Bayes估计的合理性并对比分析不同损失函数下E-Bayes估计的稳健性，得出在加权平方损失函数下的E-Bayes估计较为稳健。可以判定加权平方损失函数下逆伽马分布参数的E-Bayes估计是最优估计方法。

Abstract: In order to solve the E-Bayes estimation problem of inverse gamma distribution parameters, this paper discusses and gives the estimation of scale parameters under the square loss function and weighted square loss function for the inverse gamma distribution under the condition that the shape parameters are known. At the same time, based on Bayes estimation, the E-Bayes estimation of the corresponding parameters under the same conditions is derived, and the Monte Carlo method is used to carry out random simulation to verify the rationality of E-Bayes estimation and compare and analyze the robustness of E-Bayes estimation under different loss functions, and it is concluded that the E-Bayes estimation under the weighted squared loss function is relatively robust. The E-Bayes estimation of the inverse gamma distribution parameters under the weighted squared loss function is the optimal estimation method.