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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (6): 692-704    DOI: 10.3785/j.issn.1008-9497.2017.06.008
数学与计算机科学     
全样本场合下两参数Birnbaum-Saunders疲劳寿命分布的统计分析
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
Statistical analysis of two-parameter Birnbaum-Saunders fatigue life distribution under full sample
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
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摘要： 通过对数变换给出了求两参数Birnbaum-Saunders （BS）疲劳寿命分布BS （α，β）在全样本场合下参数的对数矩估计，并通过大量Monte-Carlo模拟比较了各种点估计方法的精度.基于对数变换通过一阶泰勒展开，将两参数BS疲劳寿命分布BS （α，β）近似看作两参数对数正态分布，由此得到了2个参数α，β的近似区间估计，通过Monte-Carlo模拟发现，所给出的近似方法比原有方法更精确.最后通过若干实例说明了方法的可行性.
关键词： 两参数Birnbaum-Saunders疲劳寿命分布;  形状参数;  刻度参数;  点估计;  近似区间估计    
Abstract: The logarithmic moment estimations of parameters are proposed by logarithmic transformation for two-parameter Birnbaum-Saunders(BS) fatigue life distribution BS(α,β) under the full sample. The precisions of various point estimation methods are compared by a large number of Monte-Carlo simulations. Two-parameter BS fatigue life distribution BS(α,β) is approximately regarded as two-parameter lognormal distribution through the first order Taylor expansion based on logarithmic transformation. Then, the approximate interval estimations of two parameters α,β are obtained, and it can be found that this approximate method is more accurate than the original method by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.
Key words: two-parameter Birnbaum-Saunders fatigue life distribution    shape parameter    scale parameter    point estimation    approximate interval estimation
收稿日期: 2016-12-07 出版日期: 2018-04-09
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.
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引用本文:

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.

XU Xiaoling, WANG Ronghua, GU Beiqing. Statistical analysis of two-parameter Birnbaum-Saunders fatigue life distribution under full sample. Journal of ZheJIang University(Science Edition), 2017, 44(6): 692-704.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.06.008    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I6/692

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