高师理科学刊2024，Vol.44Issue(12)：10-16,7.DOI:10.3969/j.issn.1007-9831.2024.12.003
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
摘要
Abstract
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Key words
type Ⅰ interval deletion/Weibull distribution/linear regression model/Monte Carlo simulation/least squares estimation分类
数理科学引用本文复制引用
李清宇,黄介武..Ⅰ型区间删失下威布尔分布的最小二乘估计[J].高师理科学刊,2024,44(12):10-16,7.基金项目
贵州省教育厅自然科学研究项目(黔教技[2022]015号) （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) （黔教技[2023]012号）
