基于β似然函数的参数估计方法

doi:10.13700/j.bh.1001-5965.2015.0071

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

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. 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. 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/Abstract

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

中图分类号:

TB114.3

王晓红, 李宇翔, 余闯, 王立志. 基于β似然函数的参数估计方法[J]. 北京航空航天大学学报, 2016, 42(1): 41-46.

WANG Xiaohong, LI Yuxiang, YU Chuang, WANG Lizhi. Parameter estimation method based on beta-likelihood function[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2016, 42(1): 41-46.

参考文献

[1] 赵军圣,庄光明,王增桂.极大似然估计方法介绍[J].长春理工大学学报,2010,5(6):53-54. ZHAO J S,ZHUANG G M,WANG Z G.An introduction about maximum likelihood estimation[J].Journal of Changchun University of Science and Technology,2010,5(6):53-54(in Chinese).
[2] BO R.The maximum spacing method:An estimation method related to the maximum likelihood method[J].Scandinavian Journal of Statistics,1984,11(2):93-112.
[3] EKSTRÖM M.On the consistency of the maximum spacing method[J].Journal of Statistical Planning and Inference,1998,70(2):209-224.
[4] GHOSH K,JAMMALAMADAKA S R.A general estimation method using spacings[J].Journal of Statistical Planning and Inference,2001,93(1):71-82.
[5] EKSTROM M.Consistency of generalized maximum spacing estimates[J].Scandinavian Journal of Statistics,2001,28(2):343-354.
[6] 孙振东,王喜山.一种计算电子元器件工作寿命的方法——最好线性无偏估计(BLUE)法[J].烟台大学学报(自然科学与工程版),1994(4):10-17. SUN Z D,WANG X S.A method to calculate lifetime of electronic devices-the best linear undistorted estimation[J].Journal of Yantai University(Natural Science and Engineering),1994(4):10-17(in Chinese).
[7] 徐安.BLUE和GLUE及主要点估计方法的评价[J].济南交通高等专科学校学报,1994(1):37-44. XU A.Assessment of BLUE and GLUE and the main point estimation method[J].Journal of Jinan Communications College,1994(1):37-44(in Chinese).
[8] SHAO Y.Consistency of the maximum product of spacing method and estimation of a unimodal distribution[J].Statistica Sinica,2001,11(4):1125-1140.
[9] EKSTRÖM M.Alternatives to maximum likelihood estimation based on spacings and the Kullback-Leibler divergence[J].Journal of Statistical Planning and Inference,2008,138(6):1778-1791.
[10] RANNEBY B,JAMMALAMADAKA S R,TETERUKOVSKIY A.The maximum spacing estimation for multivariate observations[J].Journal of Statistical Planning and Inference,2005,129(1):427-446.
[11] EL HAJE HUSSEIN F,GOLUBEV Y.On entropy estimation by m-spacing method[J].Journal of Mathematical Sciences,2009,163(3):290-309.
[12] GOMES A E,DA SILVA C Q,CORDEIRO G M.The beta Burr III model for lifetime data[J] Brazilian Journal of Probability and Statistics,2013,27(4):502-543.
[13] BADSHA MD.B,MOLLAH MD.N H,JAHAN N,et al.Robust complementary hierarchical clustering for gene expression data analysisby β-divergence[J].Journal of Bioscience and Bioengineering,2013,116(3):397-407.
[14] CORDEIRO G M,NADARAJAH S,ORTEGA E M M.General results for the beta Weibull distribution[J].Journal of Statistical Computation and Simulation,2013,83(6):1082-1114.
[15] CORDEIRO G M,LEMONTE A J.The β-Birnbaum-Saunders distribution:An improved distribution for fatigue life modeling[J].Computational Statistics and Data Analysis,2011,55(3):1445-1461.
[16] PARANAÍBA P F,ORTEGA E M M,CORDEIRO G M,et al.The beta Burr XII distribution with application to lifetime data[J].Computational Statistics and Data Analysis,2011,55(2):1118-1136.
[17] SILVA G O,ORTEGA E M M,CORDEIRO G M.The beta modified Weibull distribution[J].Lifetime Data Analysis,2010,16(3):409-430.
[18] 赵宇,杨军,马小兵.可靠性数据分析教程[M].北京:北京航空航天大学出版社,2009:150-151. ZHAO Y,YANG J,MA X B.Data analysis of reliability[M].Beijing:Beihang Uuiversity Press,2009:150-151(in Chinese).
[19] 周品,赵新芬.MATLAB数理统计分析[M].北京:国防工业出版社,2009:200-204. ZHOU P,ZHAO X F.MATLAB statistics analysis[M].Beijing:National Defense Industry Press,2009:200-204(in Chinese).

基于β似然函数的参数估计方法

Parameter estimation method based on beta-likelihood function

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