逆高斯分布参数的线性贝叶斯估计

发布时间：2018-05-01 15:19

本文选题：逆高斯分布 + 线性贝叶斯估计　；参考：《北京交通大学》2017年硕士论文

【摘要】：逆高斯分布具有许多优良的特性,在寿命试验、管理科学、精算学等众多领域应用广泛。针对逆高斯分布参数的估计问题,国内外学者已经做了大量的研究,提出了许多估计方法,常用的有极大似然估计、无偏估计和贝叶斯估计等。本文提出了一种新的参数估计方法—线性贝叶斯估计,其主要的思想是利用样本统计量的线性表达估计参数。应用此方法本文分别求解出了三个统计量X、T和XT以及五个统计量X、T、XT、X2和T2下的线性贝叶斯估计表达式,并在均方误差矩阵准则下,证明了五个统计量下的线性贝叶斯估计要优于三个统计量下的线性贝叶斯估计,也证明了不同个数统计量下所得到的线性贝叶斯估计都要优于经典的极大似然估计和无偏估计。通常对参数进行贝叶斯估计时,由于计算过程中积分的复杂性,常常难以得到贝叶斯估计的显式解,为此一般采用MCMC方法获得贝叶斯估计。本文数值模拟部分也考察了 Lindley近似计算方法,计算出了平方损失函数下贝叶斯估计的近似表达式。在给定不同先验分布的情形下,分别对三个统计量、五个统计量下的线性贝叶斯估计与贝叶斯估计之间的距离,以及Lindley近似结果与贝叶斯估计之间的距离进行数值模拟。通过对模拟结果的分析,进一步验证了统计量个数越多所得到的线性贝叶斯估计效果越好。
[Abstract]:Inverse Gao Si distribution has many excellent properties and is widely used in many fields such as life test, management science, actuarial science and so on. For the estimation of inverse Gao Si distribution parameters, scholars at home and abroad have done a lot of research and put forward many estimation methods, such as maximum likelihood estimation, unbiased estimation and Bayesian estimation. In this paper, a new parameter estimation method, linear Bayesian estimation, is proposed. Its main idea is to estimate the parameters by using the linear expression of sample statistics. By using this method, the linear Bayesian estimation expressions for three statistics XT and XT and five statistics XT _ T _ 2 and T _ 2 are obtained, respectively, and under the mean square error matrix criterion, the linear Bayesian estimators are obtained. It is proved that the linear Bayesian estimators under five statistics are superior to the linear Bayesian estimators under three statistics, and that the linear Bayesian estimators under different numbers of statistics are superior to the classical maximum likelihood estimators and unbiased estimators. When Bayesian estimation of parameters is usually carried out, it is often difficult to obtain the explicit solution of Bayesian estimation because of the complexity of the integral in the calculation process. Therefore, the Bayesian estimation is usually obtained by using MCMC method. In the part of numerical simulation, the approximate expression of Bayesian estimation based on square loss function is calculated. In the case of different prior distributions, the distance between the linear Bayesian estimator and the Bayesian estimator under five statistics and the distance between the Lindley approximation result and the Bayesian estimation are numerically simulated. Through the analysis of the simulation results, it is further verified that the more the number of statistics, the better the effect of linear Bayesian estimation.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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