基于改进平均秩的最小二乘参数估计方法  

LEAST SQUARES ESTIMATION METHOD BASED ON THE IMPROVED MEAN RANK

作　　者：薛光明 宁鹏 钱明军[1] 何弘瑞 周军[1] XUE GuangMing;NING Peng;QIAN MingJun;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2期380-385,共6页Journal of Mechanical Strength

基　　金：军内科研项目资助。

摘　　要：针对小样本情形下传统平均秩或中位秩估计法计算精度较低的问题,采用秩估计函数修正原理,调整自然平均秩适用点,提出一种改进平均秩作为样本的累积分布函数。采用对累积分布函数直接拟合方式执行最小二乘估计,并基于威布尔分布和小样本假设,通过蒙特卡罗仿真对比不同秩估计下的参数估计效果。结果表明,对于不同参数下的威布尔分布,样本量不小于4时的改进平均秩计算尺度参数相对误差小于9.5%,计算平均失效间隔时间相对误差小于8.7%,对比传统方法计算相对误差高于16%而言,此方法可有效提升威布尔分布的参数估计精度。To improve estimating accuracy in the traditional mean rank or median rank estimation method,an improved mean rank is proposed in the correction principle of rank estimation function as the cumulative distribution function of samples by adjusting the applicable points of natural mean rank.Then a least squares estimation is performed by directly fitting the cumulative distribution function.Based on the hypothesis of Weibull distribution under small sample,the parameter estimations under different ranks are calculated by Monte Carlo simulation.The results indicate that the relative error on calculating scale parameter using the improved mean rank method for the Weibull distribution with different parameters is less than 9.5% under the condition of sample size not less than 4.Furthermore,the relative error on calculating mean time between failures using the improved mean rank method is less than 8.7%,while the relative errors using traditional methods are higher than 16%.From calculated results,proposed method can effectively improve the parameter estimation accuracy for Weibull distribution.

关 键 词：改进平均秩 最小二乘法 威布尔分布 平均失效时间 小样本 蒙特卡罗仿真 

分 类 号：TB114.3[理学—概率论与数理统计]