三参数Weibull分布的广义信仰推断  

Generalized Fiducial Inference for the Three-Parameter Weibull Distribution

作　　者：邵泽 闫亮 李梦涵 蔡霞[3] SHAO Ze;YAN Liang;LI Menghan;CAI Xia(College of Statistics and Mathematics,Heibei University of Economics and Business,Shijiazhuang 050061;Finance and Enterprise Innovation Research Center,Hebei University of Economics and Business,Shijiazhuang 050061;School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018)

机构地区：[1]河北经贸大学统计与数学学院,石家庄050061 [2]河北经贸大学金融与企业创新研究中心,石家庄050061 [3]河北科技大学理学院,石家庄050018

出　　处：《系统科学与数学》2024年第8期2515-2535,共21页Journal of Systems Science and Mathematical Sciences

基　　金：河北省自然科学基金面上项目(A2020207006,A2022208001);河北省在读研究生创新能力培养资助项目(CXZZSS2023103);国家自然科学基金青年项目(12001155)资助课题。

摘　　要：三参数Weibull分布作为可靠性分析的常用分布之一,由于其存在非正则问题,导致频率方法的大样本性质不总成立,而贝叶斯方法在先验的选择上也会面临一些问题.为了使实际工作者多一种选择,文章将广义信仰推断应用到三参数Weibull分布的研究中,对于可靠度等感兴趣参数,构建了广义信仰点估计和置信区间,并将其与频率方法和贝叶斯方法进行比较.模拟结果表明,广义信仰点估计拥有更小或相当的均方误差,而且在保证覆盖率的基础上拥有更短或相当的平均区间长度.最后,文章使用单碳纤维强度数据和滚球轴承数据验证了广义信仰推断在三参数Weibull分布中的有效性.The three-parameter Weibull distribution is one of the commonly used distributions for reliability analysis.However,its non-regular issue poses challenges to the validity of large sample properties of frequentist method.Additionally,the selection of prior in Bayesian estimation also faces certain issues.In order to provide practitioners with an alternative choice,this paper applies the generalized fiducial inference to the study of the three-parameter Weibull distribution.For the interest parameters such as reliability,generalized fiducial point estimation and confidence interval are constructed and compared with frequentist method and Bayesian method.Simulation results show that generalized fiducial point estimation has smaller or comparable mean square error and shorter or comparable average interval length while maintaining coverage probability.Finally,the effectiveness of generalized fiducial inference in the three-parameter Weibull distribution is demonstrated using data on single carbon fibers strength and ball bearings.

关 键 词：三参数WEIBULL分布 最大间隔积估计 贝叶斯估计 广义信仰推断 可靠度 

分 类 号：O212.1[理学—概率论与数理统计]