Please wait a minute...
浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (6): 691-704    DOI: 10.3785/j.issn.1008-9497.2020.06.007
数学与计算机科学     
两参数拉普拉斯BS疲劳寿命分布的统计分析
徐晓岭1, 顾蓓青1, 王蓉华2
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
Statistical analysis of two-parameter Laplace BS fatigue life distribution
XU Xiaoling1, GU Beiqing1, WANG Ronghua2
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(1308 KB)   HTML  
摘要： 研究了两参数拉普拉斯BS疲劳寿命分布LBS(α,β)的极大似然估计，指出了原文献中的错误；给出了几种参数点估计的方法，通过Monte-Carlo模拟,比较了各方法的优劣，其中，对数矩估计方法精度较高；还讨论了参数的近似区间估计，比较了2种方法参数α的近似区间估计精度。
关键词： 刻度参数;  点估计;  近似区间估计;  两参数拉普拉斯BS疲劳寿命分布;  形状参数    
Abstract: The maximum likelihood estimations of two-parameter Laplace Birnbaum-Saunders (BS) fatigue life distribution LBS(α,β) are investigated in this paper and the errors in the original literature are pointed out. Then several point estimation methods of parameters are proposed. The estimation advantages and disadvantages of point estimation methods are compared by Monte-Carlo simulations, and it is found that the method of log-moment is more accurate than others. Finally, the approximate interval estimations of parameters are discussed, and the precisions of approximate interval estimations of two methods are compared for the parameter α.
Key words: two-parameter Laplace BS fatigue life distribution    scale parameter    point estimation    approximate interval estimation    shape parameter
收稿日期: 2018-09-27 出版日期: 2020-11-25
CLC:  O 213  
基金资助: 国家自然科学基金资助项目(11671264).
通讯作者: 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.c；
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
顾蓓青
王蓉华

引用本文:

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.

XU Xiaoling, GU Beiqing, WANG Ronghua. Statistical analysis of two-parameter Laplace BS fatigue life distribution. Journal of Zhejiang University (Science Edition), 2020, 47(6): 691-704.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.06.007    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I6/691

1 BIRNBAUM Z W, SAUNDER S C. A new family of life distribution[J]. Journal of Applied Probability, 1969, 6(2): 319-327.
2 杨德滋，车惠民. 混凝土在重复荷载作用下疲劳寿命分布的概率方法研究[J]. 铁道学报,1990, 12(4): 56-65. YANG D Z, CHE H M. The probabilistic method research on the fatigue life distribution for concrete under repeated loading[J]. Journal of the China Railway Society, 1990, 12(4): 56-65.
3 DESMOND A F. Stochastic models of failure in random environments[J]. Canadian Journal of Statistics, 1985, 13(3): 171-183. DOI: 10.2307/3315148
4 DESMOND A F, On the relationship between two fatigue-life models[J]. IEEE Transactions on Reliability, 1986, 35(2): 167-169.
5 BIRNBAUM Z W, SAUNDER S C. Estimation for a family of life distribution with applications to fatigue[J]. Journal of Applied Probability, 1969, 6(2): 328-347. DOI: 10.1017/S002190020003285X
6 ENGELHARDT M, BAIN L J, 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. DOI: 10.2307/1267788
7 RIECK J R, NEDELMAN J R. A log-linear model for the Birnbaum-Saunders distribution[J]. Techanometrics, 1991, 33(1): 51-60. DOI: 10.2307/1269007
8 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(3): 283-298. DOI: 10.1016/j.csda.2004.10.014
9 DUPUIS D J, MILLS J E. Robust estimation of the Birnbaum-Saunders distribution[J]. IEEE Transactions on Reliability, 1998, 47(1): 88-95. DOI: 10.1109/24.690913
10 CHANG D S, TANG L C. Reliability bounds and critical time for the Birnbaum-Saunders distribution[J]. IEEE Transactions on Reliability, 1993, 42(3): 464-469. DOI: 10.1109/24.257832
11 RIECK J R. Parametric estimation for the Birnbaum-Saunders distribution based on symmetrically censored samples[J]. Communication in Statistics-Theory and Methods, 1995, 24(7): 1721-1736. DOI: 10.1080/03610929508831581
12 OWEN W J, PADGETT W J. A Birnbaum-Saunders accelerated life model[J]. IEEE Transactions on Reliability, 2000, 49(2): 224-229. DOI: 10.1109/24.877342
13 OWEN W J, PADGETT W J. Acceleration models for system strength based on Birnbaum-Saunders distribution[J]. Lifetime Data Analysis,1999, 5(2): 133-147. DOI: 10.1023/A:1009649428243
14 OWEN W J, PADGETT W J. Power-law accelerated Birnbaum-Saunders life models[J]. International Journal of Raliability Quality and Safety Engineering, 2000, 7(7)：1-15.
15 KUNDU D, KANNAN N, BALAKRISHNAN N. On the hazard function of Birnbaum-Saunders distribution and associated inference[J]. Computational Statistics and Data Analysis, 2008, 52(5): 2692-2702. DOI: 10.1016/j.csda.2007.09.021
16 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. DOI: 10.3321/j.issn:1000-1093.2009.11.028 SUN Z L. Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J]. Acta Armamentarli, 2009，30(11)：1558-1561. DOI: 10.3321/j.issn:1000-1093.2009.11.028
17 WANG B X. Generalized interval estimation for the Birnbaum-Saunders distribution[J]. Computational Statistics and Data Analysis, 2012, 56(12): 4320-4326. DOI: 10.1016/j.csda.2012.03.023
18 NIU C Z, GUO X, XU W L, et al, Comparison of several Birnbaum-Saunders distributions[J]. Journal of Statistical Computation and Simulation, 2014, 84(12): 2721-2733. DOI: 10.1080/00949655.2014.88 1814
19 王蓉华，顾蓓青，徐晓岭. 两参数BS疲劳寿命分布的拟合检验以及环境因子的近似区间估计[J]. 上海师范大学学报, 2019, 48(4): 339-346. WANG R H, GU B Q, XU X L. Fitting test of two-parameter BS fatigue life distribution and approximate interval estimation of environmental factor[J]. Journal of Shanghai Normal University(Natural Sciences), 2019, 48(4): 339-346.
20 GARCIA J A, SANCHEZ V E L, A new family of life distributions based on the elliptically contoured distributions[J]. Journal of Statistical Planning and Inference, 2005, 128(2): 445-457.
21 SANHUEZA A, LEIVA V, BALAKRISHNAN N. The generalized Birnbaum-Saunders distribution and its theory, methodology and application[J]. Communications in Statistics-Theory and Methods, 2008, 37(5): 645-670. DOI 10.1080/0361092070154 1174
22 BARROS M, PAULA G A, LEIVA V. An R implementation for generalized Birnbaum-Saunders distributions[J]. Computational Statistics and Data Analysis, 2009, 53(4): 1511-1528. DOI: 10.1016/j.csda.2008.11.005
23 ZHU X J, BALAKRISHNAN N. Birnbaum-Saunders distribution based on Laplace kernel and some properties and inferential issues[J]. Statistics and Probability Letters, 2015, 101：1-10. DOI: 10.1016/j.spl.2015.02.007
24 徐晓岭, 王蓉华. 概率论与数理统计[M]. 北京: 人民邮电出版社, 2014: 48-52. XU X L, WANG R H. Probability and Mathematical Statistics[M]. Beijing: Posts and Telecom Press, 2014: 48-52.
25 WANG R H, FEI H L. Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type-II bilateral censoring and multiply type-II censoring[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(2): 126-132.
26 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. DOI: 10.3785/j.issn.1008-9497.2016.05.008 XU X L, WANG R H, GU B Q. Two notes of statistical analysis about two-parameter Birnbaum-Saunders fatigue life distribution[J]. Journal of Zhejiang University (Science Edition), 2016, 43(5): 539-544. DOI: 10.3785/j.issn.1008-9497.2016.05.008
[1] 孔翔,陈军. 一类带4个形状参数的同次三角曲面构造算法[J]. 浙江大学学报（理学版）, 2023, 50(2): 153-159.
[2] 王海波, 杨当福, 佘卫勤, 刘圣军, 刘新儒, 陈月安, 白燕羽. 带2个形状参数的多项式可展曲面造型[J]. 浙江大学学报（理学版）, 2021, 48(2): 131-142.
[3] 张迪, 查东东, 刘华勇. 三次DP曲线定义区间的扩展及其形状优化[J]. 浙江大学学报（理学版）, 2020, 47(2): 178-190.
[4] 严兰兰, 樊继秋. 保形分段三次多项式曲线的形状分析[J]. 浙江大学学报（理学版）, 2018, 45(1): 44-53.
[5] 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.
[6] 李军成, 宋来忠. 利用带形状参数的有理势函数构造基于Metaball的过渡曲线[J]. 浙江大学学报（理学版）, 2017, 44(3): 307-313.
[7] 严兰兰， 应正卫. 具有简单G3条件的可调曲线曲面[J]. 浙江大学学报（理学版）, 2016, 43(1): 87-96.