北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (1): 41-46.doi: 10.13700/j.bh.1001-5965.2015.0071

• 论文 • 上一篇    下一篇

基于β似然函数的参数估计方法

王晓红1, 李宇翔1, 余闯1, 王立志2   

  1. 1. 北京航空航天大学可靠性与系统工程学院, 北京 100083;
    2. 北京航空航天大学无人驾驶飞行器研究所, 北京 100083
  • 收稿日期:2015-01-31 出版日期:2016-01-20 发布日期:2016-01-28
  • 通讯作者: 王晓红,Tel.:010-82338032E-mail:wxhong@buaa.edu.cn E-mail:wxhong@buaa.edu.cn
  • 作者简介:王晓红女,博士,副教授。主要研究方向:可靠性试验与评估技术。Tel.:010-82338032E-mail:wxhong@buaa.edu.cn
  • 基金资助:
    航空科学基金 (2014ZC51031)

Parameter estimation method based on beta-likelihood function

WANG Xiaohong1, LI Yuxiang1, YU Chuang1, WANG Lizhi2   

  1. 1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. Research Institute of Unmanned Aerial Vehicle, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2015-01-31 Online:2016-01-20 Published:2016-01-28
  • Supported by:
    Aeronautical Science Foundation of China (2014ZC51031)

摘要: 分布参数估计是可靠性数据分析的手段,用于研究产品可靠性的变化规律及评估产品的可靠性水平。使用寿命试验中产品可靠度所服从的β分布评价可靠度估计值的合理程度,认为可靠度估计值在β分布中概率密度较大的更合理,给出了一种评价可靠度函数估计好坏的β似然函数,探讨了使用该函数进行分布参数估计的β似然估计方法,通过仿真验证了该方法在指数分布和威布尔分布下的适用性,并给出了应用实例。本参数估计方法理论依据充分,适用于各种分布类型,估计结果合理可信。极大似然估计方法以样本在待估分布中的概率密度作为评价准则,与之不同,本方法以累积发生比例的估计值作为评价准则,更适用于可靠性、生存率等关注事件累积发生比例的场合。

关键词: 参数估计, &beta, 分布, 可靠性数据分析, 寿命分布, &beta, 似然函数

Abstract: Distribution parameter estimation is a common method which is used in reliability data analysis to study the change rules of product reliability and evaluate the reliability level of the product. Learning from the beta distribution which is used to describe the product reliability in life test and evaluate the reasonable degree of estimator of reliability, we thought that reliability estimator is more reasonable if its probability density function is bigger in the beta distribution, raised a beta likelihood function to evaluate the reasonable level of the estimate in reliability analysis, discussed the distribution parameter estimation method when using this beta likelihood function, verified the method by simulation under the exponential distribution case and Weibull distribution case, and gave the corresponding application examples. The estimation method is based on abundant theoretic evidence, and is suitable for all kinds of distribution types. From the application examples, we know that estimation results are reasonable and believable. Maximum likelihood estimation method takes the samples' probability density function in the distribution to be estimated as the evaluation criteria, while, on the contrast, our method takes the cumulative incidence estimator as the evaluation criteria. So it is more applicable in the research on reliability and survival problems when concerning the cumulative occurrences.

Key words: parameter estimation, beta distribution, reliability data analysis, life distribution, beta-likelihood function

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