截尾数据线性回归分析方法

提出一种新的回归分析方法,建立了截尾数据回归方程,给出回归系数和标准差的最佳无偏整体估计及其协方差矩阵。文中详细讨论了工程中最常见的正态分布截尾数据一元线性回归分析,给出其回归曲线的置信限和百分位值的置信区间估计,并将该方法推广到极值分布和威布尔分布的情况。传统回归分析只适用于来自正态分布的完全数据,对于截尾数据或威布尔分布数据则无能为力,目前工程上只能采用成组试验方法,结果导致试验量很大。本文方法能够很好地解决上述问题,与成组试验法相比,在试样数相同的条件下具有更高的精度,而在精度相同的情况下,则可以节省大量试样。

Linear Regression Analysis Method for Censored Data

A new regression analysis method is presented and the regression equation for censored data is established. The best unbiased integral estimators for the regression parameters,the standard deviation and their covariance are also given.The confidence limits of the regression curve and the confidence intervals of percentiles for normal distributions are discussed in detail.The traditional regression analysis is only suitable to complete data from normal distribution.In engineering,censored data is analyzed by group test method that requires a large number of samples.The present method extends traditional regression analysis to not only censored data but also extreme distribution and Weibull distribution.Compared with traditional method,the present method can reach a higher precision and a great number of specimens can be saved.