正态分布置信检验方法

Confidence Test Method for Normal Distribution

正态母体特征值(母体均值、百分位值、百分率、标准差和变异系数等)的检验是工程中常见的问题。本文根据置信检验理论,建立了正态母体特征值的置信检验方法,包括母体均值、百分位值、百分率、标准差和变异系数的强检验、弱检验和弱强检验,可以满足不同的实际需求。置信检验克服了显著性假设检验在接受原假设时缺乏说服力的弱点,能够以高概率判断正态母体特征值是否满足工程中规定的条件。不但比传统的正态分布假设检验和抽样检验具有更高的精度,而且更加便于应用,许多假设检验和抽样检验难以处理的问题(如母体百分率和百分位值的检验),采用置信检验可以容易地得到解决。

The normal population characteristics, such as the mean, standard deviation, percentile, percentage and coefficient of variation, are often tested in engineering. Based on the theory of confidence tests, the test methods for normal population characteristics are presented in this paper, which include the strong test, the weak test and the weak-strong test. Compared with the hypothesis tests and sampling inspections for normal distribution, the confidence tests can overcome the disadvantage that to accept a null hypothesis may simply mean that it is not rejected by significance hypothesis tests, and greatly improve the test precision. The confidence tests can also bring more convenience in engineering, as that the tests for the percentile and percentage of normal population that are difficult in hypothesis tests can be easily solved by the present method.