复合Mlinex损失函数下艾拉姆咖分布参数的Bayes估计  

Bayes Estimation of Alamka Distribution Parameters under Compound Mlinex Loss Function

作　　者：杜丽芳 张艳 何腾松 

机构地区：[1]贵州师范大学数学科学学院,贵州 贵阳

出　　处：《理论数学》2024年第5期153-162,共10页Pure Mathematics

摘　　要：在本文中,我们采用了一种复合的Mlinex损失函数作为研究的基础准则,艾拉姆咖是一种衡量统计模型优良性的指标,通常用于模型选择。当我们在模型中引入逆伽玛分布作为先验分布时,我们利用Mlinex损失函数来评估艾拉姆咖指标的表现,并且讨论了该分布下三种不同的参数估计方法:Bayes估计、E-Bayes估计和多层Bayes估计。为了验证这些估计方法的性能,本文采用了数值模拟的方法。通过构建模拟数据集,并应用上述估计方法,可以观察它们在不同情况下的表现。模拟结果显示,这三种估计方法都表现出了良好的稳健性。In this paper, we use a composite Mlinex loss function as the basic criterion for the study. Alamka is a measure of the goodness of statistical models, which is often used for model selection. When we introduce the inverse gamma distribution as a prior distribution into the model, we use the Mlinex loss function to evaluate the performance of the Alamba index, and discuss three different parameter estimation methods under this distribution: Bayes estimation, E-Bayes estimation, and multilayer Bayes estimation. In order to verify the performance of these estimation methods, numerical simulation is used in this paper. By building simulated datasets and applying the above estimation methods, it is possible to observe how they perform in different situations. The simulation results show that these three estimation methods have good robustness.

关 键 词：复合Mlinex损失函数 艾拉姆咖分布 BAYES估计 E-BAYES估计 多层BAYES估计 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]