步加试验下Pareto分布的统计分析

发布时间：2018-01-09 15:23

本文关键词：步加试验下Pareto分布的统计分析　出处：《温州大学》2016年硕士论文　论文类型：学位论文

【摘要】：Pareto分布最初是模拟经济失效数据,但随着科技的发展,Pareto分布已经广泛应用于可靠性寿命试验中。许多文献对Pareto分布的可靠性进行了统计分析,但尚未有文献用lindly方法对二型双参数Pareto分布进行贝叶斯估计,本文将对步进压力下不同加速模型的二型双参数Pareto分布进行统计研究,用lindly方法对其进行贝叶斯估计,最后通过数据模拟对不同方法下得出的参数进行比较,以检验试验方法的有效性。文中主要研究如下三个内容:1、对CE模型下二型双参数Pareto分布在步进压力定时截尾试验下进行了研究,在极大似然估计(MLE)中似然函数的参数减少为单一的非线性方程进行求解,同时基于似然函数的渐近正态性得到参数的近似置信区间(ACI);在贝叶斯估计中,由于参数不能用显式形式表达,因此我们采用Lindly方法对参数进行近似估计,并运用MCMC方法得到了参数的置信区间(CRI),最后用两种方法对数据进行模拟比较得出结论。2、对TRV模型下二型双参数Pareto分布在步进压力下逐次截尾试验进行了统计分析,通过对参数进行极大似然估计,及似然函数的渐近正态性得到参数估计值和区间估计,利用无信息先验对参数进行贝叶斯估计。3、对TFR模型下二型双参数Pareto分布在步进压力下逐次截尾试验进行了统计分析,利用极大似然估计和贝叶斯估计分别对参数进行了估计,并对两种方法下得出的参数值进行了比较。最后对本文所研究的工作进行了总结,并提出了一些新的建议。
[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.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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