發(fā)布時(shí)間：2018-01-09 15:23

  本文關(guān)鍵詞：步加試驗(yàn)下Pareto分布的統(tǒng)計(jì)分析　出處：《溫州大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Pareto分布 極大似然估計(jì) 貝葉斯估計(jì) lindly方法

【摘要】：Pareto分布最初是模擬經(jīng)濟(jì)失效數(shù)據(jù),但隨著科技的發(fā)展,Pareto分布已經(jīng)廣泛應(yīng)用于可靠性壽命試驗(yàn)中。許多文獻(xiàn)對(duì)Pareto分布的可靠性進(jìn)行了統(tǒng)計(jì)分析,但尚未有文獻(xiàn)用lindly方法對(duì)二型雙參數(shù)Pareto分布進(jìn)行貝葉斯估計(jì),本文將對(duì)步進(jìn)壓力下不同加速模型的二型雙參數(shù)Pareto分布進(jìn)行統(tǒng)計(jì)研究,用lindly方法對(duì)其進(jìn)行貝葉斯估計(jì),最后通過(guò)數(shù)據(jù)模擬對(duì)不同方法下得出的參數(shù)進(jìn)行比較,以檢驗(yàn)試驗(yàn)方法的有效性。文中主要研究如下三個(gè)內(nèi)容:1、對(duì)CE模型下二型雙參數(shù)Pareto分布在步進(jìn)壓力定時(shí)截尾試驗(yàn)下進(jìn)行了研究,在極大似然估計(jì)(MLE)中似然函數(shù)的參數(shù)減少為單一的非線性方程進(jìn)行求解,同時(shí)基于似然函數(shù)的漸近正態(tài)性得到參數(shù)的近似置信區(qū)間(ACI);在貝葉斯估計(jì)中,由于參數(shù)不能用顯式形式表達(dá),因此我們采用Lindly方法對(duì)參數(shù)進(jìn)行近似估計(jì),并運(yùn)用MCMC方法得到了參數(shù)的置信區(qū)間(CRI),最后用兩種方法對(duì)數(shù)據(jù)進(jìn)行模擬比較得出結(jié)論。2、對(duì)TRV模型下二型雙參數(shù)Pareto分布在步進(jìn)壓力下逐次截尾試驗(yàn)進(jìn)行了統(tǒng)計(jì)分析,通過(guò)對(duì)參數(shù)進(jìn)行極大似然估計(jì),及似然函數(shù)的漸近正態(tài)性得到參數(shù)估計(jì)值和區(qū)間估計(jì),利用無(wú)信息先驗(yàn)對(duì)參數(shù)進(jìn)行貝葉斯估計(jì)。3、對(duì)TFR模型下二型雙參數(shù)Pareto分布在步進(jìn)壓力下逐次截尾試驗(yàn)進(jìn)行了統(tǒng)計(jì)分析,利用極大似然估計(jì)和貝葉斯估計(jì)分別對(duì)參數(shù)進(jìn)行了估計(jì),并對(duì)兩種方法下得出的參數(shù)值進(jìn)行了比較。最后對(duì)本文所研究的工作進(jìn)行了總結(jié),并提出了一些新的建議。
[Abstract]:Pareto distribution was initially used to simulate economic failure data, but with the development of science and technology. Pareto distribution has been widely used in reliability life test. Many literatures have made statistical analysis on the reliability of Pareto distribution. However, lindly method has not been used to estimate the two-parameter Pareto distribution in literature. In this paper, the two-parameter Pareto distribution of two types of acceleration models under stepping pressure is statistically studied, and the Bayesian estimation is carried out by using the lindly method. Finally, the parameters obtained under different methods are compared through data simulation to verify the effectiveness of the test method. The main research in this paper is as follows: 1. The two type and two parameter Pareto distribution under CE model is studied under step pressure timing truncation test. The parameters of the likelihood function are reduced to a single nonlinear equation and the approximate confidence interval of the parameters is obtained based on the asymptotic normality of the likelihood function. In Bayesian estimation, because the parameters can not be expressed in explicit form, we use the Lindly method to approximate the parameters. The confidence interval of the parameters is obtained by using MCMC method. Finally, two methods are used to simulate and compare the data. The statistical analysis of the two-parameter Pareto distribution in TRV model under stepwise pressure was carried out, and the maximum likelihood estimation of the parameters was carried out. And the asymptotic normality of the likelihood function is used to obtain the parameter estimation value and interval estimation. The Bayesian estimation of the parameters is carried out by using the uninformed priori. 3. The two-parameter two-parameter Pareto distribution in TFR model is statistically analyzed under stepwise pressure, and the parameters are estimated by maximum likelihood estimation and Bayesian estimation, respectively. Finally, the work of this paper is summarized and some new suggestions are put forward.
【學(xué)位授予單位】：溫州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.1

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本文編號(hào)：1401946