数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 664-673.

• 论文 • 上一篇    下一篇

不同损失函数下Poisson分布参数的E-Bayes估计及其E-MSE

韩明()   

  1. 宁波工程学院理学院 浙江宁波 315211
  • 收稿日期:2018-02-01 出版日期:2019-06-26 发布日期:2019-06-27
  • 作者简介:韩明, hanming618@21cn.com
  • 基金资助:
    浙江省自然科学基金(LY18A010026)

E-Bayesian Estimation and Its E-MSE of Poisson Distribution Parameter Under Different Loss Functions

Ming Han()   

  1. School of Science, Ningbo University of Technology, Zhejiang Ningbo 315211
  • Received:2018-02-01 Online:2019-06-26 Published:2019-06-27
  • Supported by:
    the Natural Science Foundation of Zhejiang Province(LY18A010026)

摘要:

为了度量E-Bayes估计的误差,该文基于E-Bayes估计的定义,引入了E-Bayes估计的E-MSE(expected mean square error)的定义.对Poisson分布的参数,在不同损失函数(包括:平方损失,K-损失,加权平方损失)下分别给出了E-Bayes估计及其E-MSE的表达式.用MonteCarlo方法进行模拟比较提出的估计方法的性能,分析了一个真实数据集并进行了比较,所得结果比较基于E-MSE,结果表明该文提出的方法可行且便于应用.

关键词: Poisson分布, E-Bayes估计, E-MSE, 损失函数, Monte Carlo方法

Abstract:

In order to measure the error of E-Bayesian estimation, this paper the definition of E-MSE(expected mean square error) is introduced based on the definition of E-Bayesian estimation. For parameter of Poisson distribution, under different loss functions (including:squared error loss, K-loss and weighted squared error loss), the formulas of E-Bayesian estimation and formulas of E-MSE are given respectively. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and a real data set have been analysed for illustrative purposes, results are compared on the basis of E-MSE, the results show that the proposed method is feasible and convenient for application.

Key words: Poisson distribution, E-Bayesian estimation, E-MSE, Loss function, Monte Carlo method

中图分类号: 

  • O213.2