Ⅰ型区间删失下威布尔分布的最小二乘估计  

Least squares estimation of Weibull distribution with type I interval deletion

作　　者：李清宇 黄介武 LI Qingyu;HUANG Jiewu(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《高师理科学刊》2024年第12期10-16,共7页Journal of Science of Teachers'College and University

基　　金：贵州省教育厅自然科学研究项目(黔教技[2022]015号);贵州省高等学校大数据分析与智能计算重点实验室项目(黔教技[2023]012号)。

摘　　要：针对Ⅰ型区间删失数据无闭合形式解的问题,提出了一种基于累积分布函数性质和指数分布顺序统计量性质的参数估计方法——NLSE方法.此方法将概率分布函数转换为累积密度函数,建立了两参数威布尔分布模型,利用威布尔线性变换构建一个回归形式,运用最小二乘估计法进行参数估计.此外,添加区间样本观测数据,在NLSE方法基础上进行改进,提出了PNLSE方法.进行蒙特卡洛数值模拟,利用偏差和均方误差两个指标对NLSE方法、PNLSE方法、MLE方法进行比较评价.结果表明,所提方法与MLE方法相比具有竞争性.另外,利用一组来自PA44飞机某训练单位发动机起动机拆换数据进行实证分析,进一步验证了PNLSE方法的优越性.A parameter estimation method based on the properties of cumulative distribution function and exponential distribution order statistic,called NLSE method,is proposed to address the problem that the type I interval missing data have not closed form solutions.This method converts the probability distribution function into a cumulative density function,establishes a two parameter Weibull distribution model,constructs a regression form using Weibull linear transformation,and uses the least squares estimation method for parameter estimation.Furthermore,to enhance the method,interval-sampled observational data is incorporated into the NLSE framework,resulting in an improved method termed the PNLSE method.Monte Carlo numerical simulation was conducted to compare and evaluate the NLSE method,PNLSE method and MLE method using two indicators of deviation and mean square error.The results showed that the proposed method was competitive with the MLE method.In addition,a set of engine starter replacement data from a training unit of PA44 aircraft was used for empirical analysis to further verify the superiority of the PNLSE method.

关 键 词：Ⅰ型区间删失 威布尔分布 线性回归模型 蒙特卡洛模拟 最小二乘估计 

分 类 号：O212.1[理学—概率论与数理统计]