基于修正枢轴量方法的威布尔分布区间估计  

INTERVAL ESTIMATION OF WEIBULL DISTRIBUTION BASED ON MODIFIED PIVOTAL VARIABLE METHOD

作　　者：薛光明 宁鹏 傅耀宇 何弘瑞 周军[1] XUE GuangMing;NING Peng;FU YaoYu;HE HongRui;ZHOU Jun(PLA Troop 63969,Nanjing 211113,China)

机构地区：[1]中国人民解放军63969部队,南京211113

出　　处：《机械强度》2023年第3期633-639,共7页Journal of Mechanical Strength

基　　金：军队军内科研项目资助。

摘　　要：针对威布尔分布传统区间估计方法计算复杂且不同参数下适用性不强的问题,提出一种多参数适用的简单区间估计方法。基于威布尔分布表达式得到卡方分布枢轴量,并对其自由度进行修正;然后结合最大似然法的点估计值以及形状参数的经验估计结果,确定威布尔分布双参数的区间估计方法;同时通过蒙特卡罗仿真对区间估计置信度进行验证,分析不同参数下估计方法的适用性,并与传统的最小二乘法和极大似然区间估计结果进行对比。结果表明,提出的修正枢轴量方法计算简单,在不同参数下的计算置信度与名义置信度差距较小,且较传统方法更加有效。To solve the problems of complex calculation and weak applicability of the traditional interval estimation methods such as Weibull distribution with the different parameters,a simple interval estimation method suitable to the conditions of multi⁃parameters was proposed.Through the expression of Weibull distribution,the pivotal⁃variable obeying chi⁃square distribution was obtained and the degrees of freedom were modified.Combined with the point estimation results from maximum likelihood estimation and the empirical estimation shape parameter in the Weibull distribution,the interval estimation method of two parameters in Weibull distribution was established.The confidence of proposed interval estimation method was verified by Monte Carlo simulation,and the applicability of the method on different parameters was also analyzed.Furthermore,comparisons with the results computed from traditional least square and maximum likelihood estimation methods were carried out by using simulation.Simulation results indicated that the modified pivotal⁃variable method has simple calculation process and small deviation from predefined nominal confidence with the different parameters.Therefore,it can be concluded that proposed method executes the more effective estimation than the traditional methods.

关 键 词：威布尔分布 区间估计 置信度 蒙特卡罗仿真 修正枢轴量 

分 类 号：TB114.3[理学—概率论与数理统计]