方法对比

	柯尔莫哥洛夫-斯米尔诺夫检验	Lilliefors 正态性检验
领域	统计学	统计学
方法族	Hypothesis test	Regression model
起源年份	1933	1967
提出者	Andrey Nikolaevich Kolmogorov; Nikolai Vasilyevich Smirnov	Hubert W. Lilliefors
类型	Nonparametric goodness-of-fit test	Goodness-of-fit / normality test
开创性文献	Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell'Istituto Italiano degli Attuari, 4, 83–91.	Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown. Journal of the American Statistical Association, 62(318), 399-402.
别名	KS test, K-S test, one-sample KS test, Kolmogorov-Smirnov Testi	Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi
相关	2	5
摘要	The Kolmogorov-Smirnov (KS) test is a nonparametric goodness-of-fit test that assesses whether a sample comes from a specified theoretical distribution, such as the normal or exponential. First formalised by Andrey Kolmogorov in 1933 and further developed by Nikolai Smirnov in 1948, it compares the empirical cumulative distribution function of the observed data against a target theoretical CDF and quantifies their maximum absolute deviation.	The Lilliefors test is a goodness-of-fit test that checks whether a continuous sample comes from a normal (or exponential) distribution when the mean and variance are unknown and estimated from the data. Introduced by Hubert W. Lilliefors in 1967, it adjusts the critical values of the Kolmogorov-Smirnov test so that they remain valid once the distribution's parameters are estimated rather than known in advance.