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→Kolmogorov–Smirnov statistic Kolmogorov-Smirnov统计
In practice, the statistic requires a relatively large number of data points (in comparison to other goodness of fit criteria such as the Anderson–Darling test statistic) to properly reject the null hypothesis.
In practice, the statistic requires a relatively large number of data points (in comparison to other goodness of fit criteria such as the Anderson–Darling test statistic) to properly reject the null hypothesis.
n个独立且均匀分布（i.i.d.）的有序观测值Xi的经验分布函数Fn定义为
n个独立且均匀分布（i.i.d.）的有序观测值Xi的经验分布函数Fn定义为：
F_{n}(x)={1 \over n}\sum _{i=1}^{n}I_{[-\infty ,x]}(X_{i})
F_{n}(x)={1 \over n}\sum _{i=1}^{n}I_{[-\infty ,x]}(X_{i})
其中 {\displaystyle I_{[-\infty ,x]}(X_{i})}I_{[-\infty ,x]}(X_{i})是指标函数，如果 {\displaystyle X_{i}\leq x}X_{i}\leq x等于1，否则等于0。
其中 {\displaystyle I_{[-\infty ,x]}(X_{i})}I_{[-\infty ,x]}(X_{i})是指标函数，如果 {\displaystyle X_{i}\leq x}X_{i}\leq x等于1，否则等于0。
给定累积分布函数F（x）的Kolmogorov–Smirnov统计量为：
D_{n}=\sup _{x}|F_{n}(x)-F(x)|
D_{n}=\sup _{x}|F_{n}(x)-F(x)|