基于Anderson-Darling正态性检验的改进方法及应用

Improved Method and Application Based on Anderson-Darling Normality Test

首先介绍了 Anderson-Darling正态性检验法的基本原理,并应用稳健统计方法——用中位值(xmed)估计总体均值μ、用标准四分位间距(NIQR)估计总体标准偏差σ,来改进Anderson-Darling统计量(AD统计量)以增强其稳健性.其次利用蒙特卡罗(Monte-Carlo)随机模拟方法产生正态分布随机数,计算改进的AD统计量,重新确定改进的AD统计量的上α分位数以及对应的上尾显著点,进而给出上尾显著点表格和拟合函数曲线供统计人员使用.以长春黄金研究院有限公司在2021年度开展的金锭中金含量化学分析能力验证为例,给出了改进后该统计量的具体应用过程,结果令人满意.

This paper first introduces the basic principle of Anderson-Darling normality test and applies the robust statistical method-estimate the mean μ with the median value(x_(med))、estimate the standard deviation with standard interquartile spacing(NIQR),to improve Anderson-Darling Statistics(AD Statistics)to enhance its robustness.Secondly,using Monte-Carlo method to generate normal distribution random numbers,we calculate the improved ad statistics,and re-determine the upper tail percentage pointαfor the improved statistics AD and the corresponding upper tail significant points,and then give the upper tail significant points table and fitting function curve for statisticians to use.Taking the chemical analysis ability verification of gold content in gold ingots carried out by Changchun Gold Research Institute Co.,Ltd.in 2021 as an example,this paper gives the specific application process of the improved statistic,and the results are satisfactory.