逆瑞利分布参数的Bayes统计推断

发布时间：2018-06-22 08:27

本文选题：逆瑞利分布 + 损失函数　；参考：《新疆师范大学》2017年硕士论文

【摘要】：逆瑞利分布在寿命试验与可靠性研究中发挥着重要而广泛的作用,目前,基于该分布的统计推断问题也处于不断的完善和发展中.在统计推断理论中,贝叶斯分析是其重要内容之一,对它的应用也几乎已经贯穿到了统计的各个领域,运用Bayes理论的一些基本内容,对参数进行相关的统计推断研究是现代统计推断的一个重要方法.本文旨在研究逆瑞利分布的贝叶斯统计推断问题.本文主要包含四个部分的内容.第一部分主要介绍了贝叶斯理论的发展、研究背景及应用.论文的主要结果在第二部分至第四部分,其中,第二部分重点讨论了在几种不同损失函数下,逆瑞利分布参数的Bayes估计.主要包括:1.当参数的先验分布取伽玛分布时,求出了逆瑞利分布的后验密度函数.2.基于Bayes理论方法,分别在对称熵损失函数,Q对称熵损失函数,Mlinex损失函数,复合LINEX对称损失函数下获得了参数的Bayes估计,证明了它的可容许性,并做了数值模拟.第三部分在Jefferys无信息先验分布下,求得了逆瑞利分布中参数在Mlinex损失函数和加权平方损失函数下的最小最大(Minimax)估计.第四部分基于NA样本,求得逆瑞利分布参数的经验Bayes检验函数,并获得Bayes检验函数的渐近性质和收敛速度.
[Abstract]:The distribution of reverse Rayleigh plays an important and extensive role in life test and reliability research. At present, the problem of statistical inference based on this distribution is also in constant perfection and development. In the theory of statistical inference, Bias analysis is one of its important contents, and its application has been almost run through all the fields of statistics. Using some basic contents of Bayes theory, the statistical inference study of parameters is an important method of modern statistical inference. This paper aims to study the Bias statistical inference problem of the distribution of the reverse Rayleigh. This paper mainly contains four parts. The first part mainly introduces the development of Bias theory, the background and the application of the research. The main results of this paper are in the second part to the fourth part, of which, the second part focuses on the Bayes estimation of the inverse Rayleigh distribution parameters under several different loss functions. It mainly includes: 1. when the prior distribution of the parameters is distributed, the posterior density function of the inverse Rayleigh distribution is obtained by the Bayes theory method based on the Bayes theory, respectively. The entropy loss function, the Q symmetric entropy loss function, the Mlinex loss function and the compound LINEX symmetric loss function obtained the Bayes estimation of the parameters. The admissibility of the parameter was proved and the numerical simulation was done. The third part obtained the Mlinex loss function and the weighted square loss function in the inverse Rayleigh distribution under the Jefferys without the information prior distribution. The minimum maximum (Minimax) estimation is given. The fourth part, based on the NA sample, obtains the empirical Bayes test function of the inverse Rayleigh distribution parameter, and obtains the asymptotic properties and convergence speed of the Bayes test function.
【学位授予单位】：新疆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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