截断删失数据下二参数Weibull分布的参数估计

发布时间：2018-03-28 05:35

本文选题：二参数Weibull分布　切入点：左截断右删失数据　出处：《兰州大学》2017年硕士论文

【摘要】：Weibull分布是一种寿命分布,在可靠性领域有极为广泛的应用.在寿命实验中,因为各种原因而出现不完全数据,其中左截断右删失数据就是不完全数据的一种常见类型.本文主要研究的是在左截断右删失数据下,二参数Weibull分布的参数估计问题.在已有的研究中,使用的估计方法主要是牛顿迭代法和期望最大化算法.在截断数据较多而样本量不大时,现有的估计法比较受限于初始值的选择,而最重要的是参数估计值的精确度有待进一步提高.因为参数估计值越精确,越能使Weibull分布有效的应用于可靠性理论和失效数据分析研究中.由于牛顿下山法可以放宽对初始值的选择范围,所以本文以牛顿下山法为基础提出参数两步迭代法来估计二参数Weibull分布的参数.这一新的估计方法先利用牛顿下山法求解左截断右删失数据下二参数Weibull分布的参数估计问题,从而削弱对初始值的依赖.在此基础上,利用形状参数估计值来提高尺度参数估计值的精确度.进而达到在小样本且截断数据较多的情况下,使二参数Weibull分布的参数估计值的整体精确度提高.最后本文将新估计法应用到两个真实数据和一个模拟数据上.数值实验结果表明,新估计方法得到的估计要优于其他的估计方法.
[Abstract]:Weibull distribution is a kind of life distribution, which is widely used in the field of reliability. Left truncated right censored data is a common type of incomplete data. In this paper, we mainly study the parameter estimation of two parameter Weibull distribution under left truncated right censored data. The main estimation methods used are Newton iteration method and expectation maximization algorithm. When there are more truncated data and a small sample size, the existing estimation methods are limited by the choice of initial values. And the most important thing is that the accuracy of the parameter estimates needs to be further improved, because the more accurate the parameter estimates are, The more effectively Weibull distribution can be applied to reliability theory and failure data analysis, the wider the selection range of initial values can be extended by Newton's downhill method. In this paper, based on Newton's downhill method, a parameter two-step iterative method is proposed to estimate the parameters of two-parameter Weibull distribution. This new method uses Newton's downhill method to solve the parameter estimation problem of two-parameter Weibull distribution under left truncation and right-censored data. Therefore, the dependence on initial value is weakened. On this basis, the accuracy of scale parameter estimation is improved by using shape parameter estimator. In the case of small sample and more truncated data, The global accuracy of the parameter estimation of the two-parameter Weibull distribution is improved. Finally, the new estimation method is applied to two real data and one simulated data. The numerical results show that, The new estimation method is superior to other estimation methods.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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