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→Two-sample Kolmogorov–Smirnov test 双样本Kolmogorov–Smirnov检验
#《Kolmogorov–Smirnov的有限概率性质和离散数据的相似统计量 Bounded Probability Properties of Kolmogorov–Smirnov and Similar Statistics for Discrete Data》<ref name=Walsh63>{{Cite journal |vauthors=Walsh JE |year=1963 |title=Bounded Probability Properties of Kolmogorov–Smirnov and Similar Statistics for Discrete Data |journal=Annals of the Institute of Statistical Mathematics |volume=15 |issue=1 |pages=153–158|doi=10.1007/bf02865912}}</ref>
#《Kolmogorov–Smirnov的有限概率性质和离散数据的相似统计量 Bounded Probability Properties of Kolmogorov–Smirnov and Similar Statistics for Discrete Data》<ref name=Walsh63>{{Cite journal |vauthors=Walsh JE |year=1963 |title=Bounded Probability Properties of Kolmogorov–Smirnov and Similar Statistics for Discrete Data |journal=Annals of the Institute of Statistical Mathematics |volume=15 |issue=1 |pages=153–158|doi=10.1007/bf02865912}}</ref>
== Two-sample Kolmogorov–Smirnov test 双样本Kolmogorov–Smirnov检验 ==
==双样本Kolmogorov–Smirnov检验 ==
[[文件:KS2 Example.png|缩略图|右|关于两个样本的Kolmogorov–Smirnov统计量的图解。 红线和蓝线分别对应于经验分布函数，而黑色箭头是两样本的KS统计量。]]
[[文件:KS2 Example.png|缩略图|右|关于两个样本的Kolmogorov–Smirnov统计量的图解。 红线和蓝线分别对应于经验分布函数，而黑色箭头是两样本的KS统计量。]]
{| class="wikitable"
|-
| <math>\alpha</math> || 0.20 || 0.15 || 0.10 || 0.05 || 0.025 || 0.01 || 0.005 || 0.001
| <math>\alpha</math> || 0.20 || 0.15 || 0.10 || 0.05 || 0.025 || 0.01 || 0.005 || 0.001
|-
|-
| <math>c({\alpha})</math> || 1.073 || 1.138 || 1.224 || 1.358 || 1.48 || 1.628 || 1.731 || 1.949
| <math>c({\alpha})</math> || 1.073 || 1.138 || 1.224 || 1.358 || 1.48 || 1.628 || 1.731 || 1.949
|}
|}
一般而言：
一般而言：<ref>Eq. (15) in Section 3.3.1 of Knuth, D.E., The Art of Computer Programming, Volume 2 (Seminumerical Algorithms), 3rd Edition, Addison Wesley, Reading Mass, 1998.</ref>
同样，样本量越大，最小界限越敏感：对于给定比率的样本大小（例如<math>m=n</math>），最小界限根据其平方根的倒数来缩放两个样本的大小。
这里要注意的是两个样本检验出来的数据样本是否来自同一分布。其并未指定该共同分布是什么（例如，它是正常还是不正常）。而且关键值表已经得出。Kolmogorov–Smirnov检验没有那么有效，因为它被设计为对两个分布函数之间所有可能的差异敏感。如刊登在Journal of Nonparametric Statistics2009年刊上Marozzi, Marco (2009)的文章《Some Notes on the Location-Scale Cucconi Test》<ref>{{cite journal |last1=Marozzi |first1=Marco |title=Some Notes on the Location-Scale Cucconi Test |journal=Journal of Nonparametric Statistics |date=2009 |volume=21 |issue=5 |page=629–647 |doi=10.1080/10485250902952435 }}</ref>和刊登在Communications in Statistics – Simulation and Computation2013年刊上同样Marozzi, Marco (2009)的文章《Nonparametric Simultaneous Tests for Location and Scale Testing: a Comparison of Several Methods》<ref>{{cite journal |last1=Marozzi |first1=Marco |title=Nonparametric Simultaneous Tests for Location and Scale Testing: a Comparison of Several Methods |journal=Communications in Statistics – Simulation and Computation |date=2013 |volume=42 |issue=6 |page=1298–1317 |doi=10.1080/03610918.2012.665546 }}</ref>显示了证据，当比较两个分布函数时，最初建议同时比较位置和比例的Cucconi检验比Kolmogorov-Smirnov检验更有效。
== 为分布函数的形状设置置信极限 ==
== 为分布函数的形状设置置信极限 ==