非对称损失函数下对数伽玛分布尺度参数的Bayes估计

Bayes Estimation of Scale Parameter of Log Gamma Distribution under Asymmetric Loss Function

摘要: 损失函数和先验分布的选取在Bayes估计问题中起重要作用。已有众多学者在不同损失函数，不同先验分布下研究了对数伽玛分布尺度参数的Bayes估计问题。本文基于Quasi先验分布分别在Linex损失与熵损失函数下，研究了对数伽玛分布尺度参数的Bayes估计。并给出了其在熵损失函数下的E-Bayes估计和多层Bayes估计。最后通过数值模拟方法对各种估计结果的优良性进行比较分析，结果表明，先验分布为Quasi分布时，尺度参数θ的Linex损失函数下的Bayes估计较熵损失函数下的稳健性更好，更接近真值。

Abstract: The selection of loss function and prior distribution plays an important role in Bayes estimation. Many scholars have studied the Bayes estimation of log-gamma distribution scale parameter under different loss function and different prior distribution. Based on Quasi-prior distribution and Linex loss function and entropy loss function respectively, the Bayes of log-gamma distribution scale parameter is studied. And its E-Bayes estimation and multilayer Bayes estimation under entropy loss function are given. Finally, the numerical simulation method is used to compare the robustness of various estimation results. The results show that when the prior distribution is Quasi, the Bayes estimation under the Linex loss function of the scale parameter theta is more stable and accurate than that under the entropy loss function.