Laplace分布参数的Bayes统计推断研究
A Study of Bayes Statistical Inference for Parameter of Laplace Distribution
DOI: 10.12677/AAM.2023.127310, PDF,    科研立项经费支持
作者: 周 慧, 袁新梅：宜春学院数学与计算机科学学院，江西 宜春
关键词: Laplace分布；Bayes估计；损失函数；LINEX损失；熵损失函数；Laplace Distribution； Bayes Estimation； Loss Function； LINEX Loss； Entropy Loss Function
摘要: Laplace分布在金融研究、可靠性理论、机器学习中具有重要的作用。本文将讨论Laplace分布参数的Bayes统计推断问题。首先研究了Laplace分布参数在平方误差损失、LINEX损失和熵损失这三类损失函数下的Bayes估计问题，然后研究了基于平方误差损失函数下的风险函数的比较问题，并通过蒙特卡洛模拟考察了各类估计的优良性，最后提出在实际应用Bayes估计时，如何针对n的取值来选择合适的Bayes估计。
Abstract: Laplace distribution plays an important role in financial research, reliability theory, and machine learning. This paper will discuss the Bayes statistical inference of Laplace distribution parameters. Firstly, the Bayes estimation of the distribution parameter under scale squared error loss, LINEX loss and entropy loss is studied, and then the comparison of risk functions under square error loss function is studied and the advantages of various estimates are investigated by Monte Carlo simula-tion. Finally, how to select an appropriate Bayes estimation based on the value of n is proposed in practical application of Bayes estimation.
文章引用：周慧, 袁新梅. Laplace分布参数的Bayes统计推断研究[J]. 应用数学进展, 2023, 12(7): 3113-3120. https://doi.org/10.12677/AAM.2023.127310

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