柯尔莫哥洛夫-斯米尔诺夫检验
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柯尔莫哥洛夫-斯米尔诺夫检验(英語:Kolmogorov-Smirnov test,簡稱K-S test),是一种基于累计分布函数的非参数检验,用以检验两个经验分布是否不同或一个经验分布与另一个理想分布是否不同。本檢定以安德雷·柯尔莫哥洛夫(Kolmogorov,俄語:Колмогоров)和尼古拉·斯米尔诺夫(Smirnov,俄語:Смирнов)之名作命名。
柯尔莫哥洛夫分布
柯尔莫哥洛夫分布(kolmogorov distribution)是随机变量
柯尔莫哥洛夫-斯米尔诺夫检验的统计量形式及其在零假设下的渐近分布是由安德雷·柯尔莫哥洛夫[1]提出的。
参考文献
- Justel, A., Peña, D. and Zamar, R. (1997) A multivariate Kolmogorov-Smirnov test of goodness of fit, Statistics & Probability Letters, 35(3), 251-259.
- Eadie, W.T.; D. Drijard, F.E. James, M. Roos and B. Sadoulet. Statistical Methods in Experimental Physics. Amsterdam: North-Holland. 1971: 269–271. ISBN 0-444-10117-9.
- Stuart, Alan; Ord, Keith; Arnold, Steven [F.]. Classical Inference and the Linear Model. Kendall's Advanced Theory of Statistics 2A Sixth. London, New York: Arnold, Oxford University Press. 1999: 25.37–25.43. ISBN 0-340-66230-1. MR 1687411.
- Corder, G.W., Foreman, D.I. (2009).Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach Wiley, ISBN 978-0-470-45461-9
- Stephens, M.A. (1979) Test of fit for the logistic distribution based on the empirical distribution function, Biometrika, 66(3), 591-5.
- ^ Kolmogorov A. Sulla determinazione empirica di una legge di distribuzione. G. Inst. Ital. Attuari. 1933, 4: 83.
外部連結
- Hazewinkel, Michiel (编), Kolmogorov-Smirnov test, 数学百科全书, Springer, 2001, ISBN 978-1-55608-010-4
- Short introduction (页面存档备份,存于互联网档案馆)
- KS test explanation (页面存档备份,存于互联网档案馆)
- JavaScript implementation of one- and two-sided tests (页面存档备份,存于互联网档案馆)
- Online calculator with the K-S test (页面存档备份,存于互联网档案馆)
- Open-source C++ code to compute the Kolmogorov distribution (页面存档备份,存于互联网档案馆) and perform the K-S test (页面存档备份,存于互联网档案馆)
- Paper on Evaluating Kolmogorov’s Distribution (页面存档备份,存于互联网档案馆); contains C implementation. This is the method used in Matlab.