Please wait a minute...
浙江大学学报(理学版)  2016, Vol. 43 Issue (5): 539-544    DOI: 10.3785/j.issn.1008-9497.2016.05.008
数学与计算机科学     
关于两参数Birnbaum-Saunders疲劳寿命分布统计分析的2个注记
徐晓岭1, 王蓉华2, 顾蓓青1
1. 上海对外经贸大学 统计与信息学院, 上海 201620;
2. 上海师范大学 数理学院, 上海 200234
Two notes of statistical analysis about two-parameter Birnbaum-Saunders fatigue life distribution
XU Xiaoling1, WANG Ronghua2, GU Beiqing1
1. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China;
2. Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
 全文: PDF(606 KB)  
摘要: 通过Monte-Carlo模拟说明目前用于求解两参数Birnbaum-Saunders疲劳寿命分布尺度参数的2种方法可能无法得到尺度参数的区间估计.进一步指出,在利用广义枢轴量法给出尺度参数以及参数函数的置信区间过程中存在错误,并用反例进行了说明,同时给出了正确的证明.
关键词: 两参数Birnbaum-Saunders疲劳寿命分布尺度参数区间估计广义枢轴量    
Abstract: We know that two methods about interval estimate of scale parameter for two-parameter Birnbaum-Saunders fatigue life distribution are shown not always capable of obtaining the interval estimate of scale parameter based on the results of Monte Carlo simulations. Moreover, there is a mistake in deriving the confidence intervals of scale parameter and parameter function with the generalized pivot method. A corresponding counter example is illustrated, and the correct proof is provided.
Key words: two-parameter Birnbaum-Saunders fatigue life distribution    scale parameter    interval estimate    generalized pivotal quantity
收稿日期: 2015-12-04 出版日期: 2016-05-01
CLC:  O213  
基金资助: 国家自然科学基金资助项目(11671264).
通讯作者: 顾蓓青,ORCID:http//orcid.org/0000-0003-1539-8747,E-mail:gubeiqing@suibe.edu.cn.     E-mail: gubeiqing@suibe.edu.cn
作者简介: 徐晓岭(1965-),ORCID:http://orcid.org/0000-0002-9442-8555,男,博士,教授,主要从事应用统计研究,E-mail:xlxu@suibe.edu.cn.
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
徐晓岭
王蓉华
顾蓓青

引用本文:

徐晓岭, 王蓉华, 顾蓓青. 关于两参数Birnbaum-Saunders疲劳寿命分布统计分析的2个注记[J]. 浙江大学学报(理学版), 2016, 43(5): 539-544.

XU Xiaoling, WANG Ronghua, GU Beiqing. Two notes of statistical analysis about two-parameter Birnbaum-Saunders fatigue life distribution. Journal of ZheJIang University(Science Edition), 2016, 43(5): 539-544.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.05.008        https://www.zjujournals.com/sci/CN/Y2016/V43/I5/539

[1] BIRNBAUM Z W, SAUNDERS S C. A new family of life distribution[J]. Journal of Applied Probability,1969(6):319-322.
[2] DESMOND A F. Stochastic models of failure in random environments[J]. The Canadian Journal of Statistics,1985(2):171-176.
[3] DESMOND A F. On the relationship between two fatigue-life models[J]. IEEE Transactions on Reliability,1986(2):167-171.
[4] BIRNBAUM Z W, SAUNDERS S C. Estimation for a family of life distributions with applications to fatigue[J]. Appl Prob, 1969(6):328-347.
[5] ENGELHARDT M, WRIGHT F T. Inferences on the parameters of the Birnbaum Saunders fatigue life distribution based on maximum likelihood estimation[J]. Technometrics,1981,23(3):251-256.
[6] RIECK J R, NEDELMAN J R. A log-linear model for the Birnbaum Saunders distribution[J]. Techanometrics,1991,33(1):51-60.
[7] NG H K T, KUNDU D, BALAKRISHNAN N. Modified moment estimation for the two-parameter Birnbaum-Saunders distribution[J]. Computational Statistics and Data Analysis,2003,43:283-298.
[8] DUPUIS D J, MILLS J E. Robust estimation of the Birnbaum distribution[J]. IEEE Transactions on Reliability,1998,47(1):88-95.
[9] CHANG D S, TANG L C. Reliability bounds and critical time for the Birnbaum-Saunders distribution[J]. Reliability, IEEE Transactions on Reliability,1993,42:464-469.
[10] RIECK J R. Parametric estimation for the Birnbaum-Saunders distribution based on symmetrically censored samples[J]. Communication Statistics-Theory Methods,1995,24:1721-1736.
[11] OWEN W J, PADGETT W J. A Birnbaum-Saunders accelerated life model[J]. IEEE Transactions on Reliability,2000,49(2):224-229.
[12] OWEN W J, PADGETT W J. Acceleration models for system strength based on Birnbaum-Saunders distribution[J]. Lifetime Data Analysis,1999(5):133-147.
[13] OWEN W J, PADGETT W J. Power-law accelerated Birnbaum-Saunders life models[J]. International Journal of Reliability, Quality and Safety Engineering,2000,7(1):1-15.
[14] KUNDU D, KANNAN N, BALAKRISHNAN N. On the hazard function of Birnbaum-Saunders distribution and associated inference[J]. Computational Statistics & Data Analysis,2008,52(5):2692-2702.
[15] 王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布的参数估计[J].华东师范大学学报,1996(4):10-15. WANG Bingxing, WAGN Lingling. Parameter estimation of Birnbaum-Saunders fatigue life distribution[J]. Journal of East China Normal University,1996(4):10-15.
[16] 王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布在截尾试验情形的统计分析[J].应用概率统计,1996,12(4):369-375. WANG Bingxing, WAGN Lingling. Statistical analysis of Birnbaum-Saunders fatigue life distribution in the censored test case[J]. Applied Probability and Statistics,1996,12(4):369-375.
[17] 王蓉华,费鹤良.双边截尾场合下BS疲劳寿命分布的参数估计[J].上海师范大学学报,1999,28(2):17-22. WANG Ronghua, FEI Heliang. Parameter estimation for the BS fatigue life distribution under bilateral censoring[J]. Journal of Shanghai Normal University,1999,28(2):17-22.
[18] WANG Ronghua, FEI Heliang. Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J]. Chin Quart J of Math,2006,21(1):15-27.
[19] WANG Ronghua, FEI Heliang. Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J]. Chin Quart J of Math,2004,19(2):126-132.
[20] 孙祝岭.Birnbaum-Saunders疲劳寿命分布尺度参数的区间估计[J].兵工学报,2009,30(11):1558-1561. SUN Zhuling. Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J]. Acta Armamentarii,2009,30(11):1158-1561.
[21] 孙祝岭.Birnbaum-Saunders疲劳寿命分布参数的回归估计方法[J].兵工学报,2010,31(9):1260-1262. SUN Zhuling. Regression estimation method of parameters for Birnbaum-Saunders fatigue life distribution[J]. Acta Armamentarii,2010,31(9):1260-1262.
[22] 孙祝岭.疲劳寿命分布变异系数的统计推断[J].质量与可靠性,2013(1):13-15. SUN Zhuling. Statistical inference of variable coefficient for fatigue life distribution[J]. Quality and Reliability,2013(1):13-15.
[23] 孙祝岭. Birnbaum-Saunders分布环境因子
[1] 徐晓岭, 顾蓓青, 王蓉华. 两参数拉普拉斯BS疲劳寿命分布的统计分析[J]. 浙江大学学报(理学版), 2020, 47(6): 691-704.
[2] 徐晓岭, 王蓉华, 顾蓓青. 两参数Birnbaum-Saunders疲劳寿命分布图像特征的拓展分析[J]. 浙江大学学报(理学版), 2019, 46(1): 22-31.
[3] 徐晓岭, 王蓉华, 顾蓓青. 全样本场合下两参数Birnbaum-Saunders疲劳寿命分布的统计分析[J]. 浙江大学学报(理学版), 2017, 44(6): 692-704.