Mlinex损失函数下基于截尾数据指数分布参数的估计

发布时间：2018-03-09 14:33

本文选题：Bayes估计　切入点：定数截尾　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着统计决策理论和贝叶斯理论的不断发展,不同损失函数下分布参数的Bayes估计问题一直是很多学者的研究方向.现如今,产品的可靠性分析越来越受到人们的重视,关于指数分布参数的统计推断问题已经有大量的文献进行了研究,但是对在截尾情形下参数估计的研究相对较少.2003年Podder C.K.和Roy M.K.提出Mlinex损失函数,引起了许多学者的广泛关注.因此本文在前人的研究基础上,选取Mlinex损失函数,分析截尾情形下指数分布参数的Bayes估计的相关问题,例如容许性问题及经验Bayes估计等.本文首先运用参数估计方法,得出在Mlinex损失函数下定数截尾情形下的MRE估计、Bayes估计的一般形式,以及当先验分布给定时Bayes估计的精确形式,较为全面地讨论了相关估计量在Mlinex损失函数下的容许性,并在超参数部分未知和完全未知两种情况下构造了刻度参数的参数型经验Bayes估计,然后运用Matlab软件进行相关数值模拟,结果表明了估计方法的可行性.接着,求出了定时截尾情形下指数分布参数在Mlinex损失函数下的Bayes估计,并证明了Bayes估计的可容许性,并进行数值模拟.最后对本文做出了总结并提出研究展望.
[Abstract]:With the statistical decision theory and Bias's theory of continuous development, Bayes parameter distribution under different loss functions estimation problem has been the research direction of many scholars. Nowadays, the reliability analysis of products more and more attention, a statistical index distribution parameter inference problem has a large number of the research literature, but the study of in case of truncation parameter estimation in.2003 Podder C.K. and less Roy M.K. proposed Mlinex loss function, attracted attention of many scholars. Therefore, this paper based on previous studies, select the Mlinex loss function, analysis of problems related to Bayes parameter estimation for exponential distribution under censoring, such as compatibility problems and experience Bayes estimation. This paper uses the parameter estimation method, obtained under Mlinex loss function censored case MRE estimation, Bayes estimation of a As a form, and when the prior distribution to form accurate timing Bayes estimation, comprehensively discusses the admissibility under Mlinex loss function correlation estimator, parametric empirical Bayes and construct a scale parameter in the hyper parameters part of the unknown and completely unknown two cases estimated, and then the related numerical simulation by Matlab software, results show that the estimation of the feasibility of the method. Then, the timing estimation of Bayes under the condition of censoring exponential distribution parameter under Mlinex loss function, and it is proved that the Bayes estimation of admissibility, and numerical simulation. Finally, the paper makes a summary and puts forward the research prospect.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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