本文選題：逆瑞利分布 + 損失函數(shù)��； 參考：《新疆師范大學(xué)》2017年碩士論文

【摘要】：逆瑞利分布在壽命試驗(yàn)與可靠性研究中發(fā)揮著重要而廣泛的作用,目前,基于該分布的統(tǒng)計(jì)推斷問(wèn)題也處于不斷的完善和發(fā)展中.在統(tǒng)計(jì)推斷理論中,貝葉斯分析是其重要內(nèi)容之一,對(duì)它的應(yīng)用也幾乎已經(jīng)貫穿到了統(tǒng)計(jì)的各個(gè)領(lǐng)域,運(yùn)用Bayes理論的一些基本內(nèi)容,對(duì)參數(shù)進(jìn)行相關(guān)的統(tǒng)計(jì)推斷研究是現(xiàn)代統(tǒng)計(jì)推斷的一個(gè)重要方法.本文旨在研究逆瑞利分布的貝葉斯統(tǒng)計(jì)推斷問(wèn)題.本文主要包含四個(gè)部分的內(nèi)容.第一部分主要介紹了貝葉斯理論的發(fā)展、研究背景及應(yīng)用.論文的主要結(jié)果在第二部分至第四部分,其中,第二部分重點(diǎn)討論了在幾種不同損失函數(shù)下,逆瑞利分布參數(shù)的Bayes估計(jì).主要包括:1.當(dāng)參數(shù)的先驗(yàn)分布取伽瑪分布時(shí),求出了逆瑞利分布的后驗(yàn)密度函數(shù).2.基于Bayes理論方法,分別在對(duì)稱(chēng)熵?fù)p失函數(shù),Q對(duì)稱(chēng)熵?fù)p失函數(shù),Mlinex損失函數(shù),復(fù)合LINEX對(duì)稱(chēng)損失函數(shù)下獲得了參數(shù)的Bayes估計(jì),證明了它的可容許性,并做了數(shù)值模擬.第三部分在Jefferys無(wú)信息先驗(yàn)分布下,求得了逆瑞利分布中參數(shù)在Mlinex損失函數(shù)和加權(quán)平方損失函數(shù)下的最小最大(Minimax)估計(jì).第四部分基于NA樣本,求得逆瑞利分布參數(shù)的經(jīng)驗(yàn)Bayes檢驗(yàn)函數(shù),并獲得Bayes檢驗(yàn)函數(shù)的漸近性質(zhì)和收斂速度.
[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.
【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.8

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