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Comparative studies between the Bayesian estimation and the maximum likelihood estimation of the parameter of the uniform distribution
被引：3
|作者：
Xu, Bao
[1
]
Wang, Di
[1
]
Qi, He
[1
]
机构：
[1] Jilin Normal Univ, Inst Math, Siping 136000, Jilin, Peoples R China
基金：
中国国家自然科学基金;
关键词：
uniform distribution;
geometric probability model;
probability distribution function;
probability density function;
Bayesian estimation;
conjugate prior distribution;
posterior density function;
loss function;
posterior risk function;
maximum likelihood estimation;
simulation investigation;
MSE;
mean square error;
D O I：
10.1504/IJMIC.2020.114187
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The point estimation of the parameter theta of the uniform distribution U(0, theta) is discussed. The general form of the Bayesian estimation of theta is investigated under the weighted square loss function in the framework of Bayesian statistics, and the precise form of the Bayesian estimation of theta is obtained based on the given Pareto conjugate prior distribution. The comparisons between the Bayesian estimation that obtained in the framework of Bayesian statistics and the maximum likelihood estimation that obtained in the framework of classical statistics are studied from theory and simulation respectively. Results show that the Bayesian estimation of theta under the weighted square loss function is smaller than the maximum likelihood estimation of theta in the framework of classical statistic in numerical value, and the Bayesian estimation that obtained is the maximum likelihood estimations of the corresponding functions of theta, respectively.
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页码：211 / 216
页数：6
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