本文選題：逆高斯分布 + 線性貝葉斯估計��； 參考：《北京交通大學(xué)》2017年碩士論文

【摘要】：逆高斯分布具有許多優(yōu)良的特性,在壽命試驗、管理科學(xué)、精算學(xué)等眾多領(lǐng)域應(yīng)用廣泛。針對逆高斯分布參數(shù)的估計問題,國內(nèi)外學(xué)者已經(jīng)做了大量的研究,提出了許多估計方法,常用的有極大似然估計、無偏估計和貝葉斯估計等。本文提出了一種新的參數(shù)估計方法—線性貝葉斯估計,其主要的思想是利用樣本統(tǒng)計量的線性表達估計參數(shù)。應(yīng)用此方法本文分別求解出了三個統(tǒng)計量X、T和XT以及五個統(tǒng)計量X、T、XT、X2和T2下的線性貝葉斯估計表達式,并在均方誤差矩陣準(zhǔn)則下,證明了五個統(tǒng)計量下的線性貝葉斯估計要優(yōu)于三個統(tǒng)計量下的線性貝葉斯估計,也證明了不同個數(shù)統(tǒng)計量下所得到的線性貝葉斯估計都要優(yōu)于經(jīng)典的極大似然估計和無偏估計。通常對參數(shù)進行貝葉斯估計時,由于計算過程中積分的復(fù)雜性,常常難以得到貝葉斯估計的顯式解,為此一般采用MCMC方法獲得貝葉斯估計。本文數(shù)值模擬部分也考察了 Lindley近似計算方法,計算出了平方損失函數(shù)下貝葉斯估計的近似表達式。在給定不同先驗分布的情形下,分別對三個統(tǒng)計量、五個統(tǒng)計量下的線性貝葉斯估計與貝葉斯估計之間的距離,以及Lindley近似結(jié)果與貝葉斯估計之間的距離進行數(shù)值模擬。通過對模擬結(jié)果的分析,進一步驗證了統(tǒng)計量個數(shù)越多所得到的線性貝葉斯估計效果越好。
[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.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.8

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本文編號：1829936