قارن الطرق

	اختبار كولموجوروف-سميرنوف	اختبار ليليفورس للاعتدالية	اختبار كولموجوروف-سميرنوف لعينتين
المجال	الإحصاء	الإحصاء	الإحصاء
العائلة	Hypothesis test	Regression model	Regression model
سنة النشأة	1933	1967	1948
صاحب الطريقة	Andrey Nikolaevich Kolmogorov; Nikolai Vasilyevich Smirnov	Hubert W. Lilliefors	N. V. Smirnov
النوع	Nonparametric goodness-of-fit test	Goodness-of-fit / normality test	Nonparametric two-sample distribution test
المصدر التأسيسي	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.	Smirnov, N. V. (1948). Table for Estimating the Goodness of Fit of Empirical Distributions. Annals of Mathematical Statistics, 19(2), 279-281.
الأسماء البديلة	KS test, K-S test, one-sample KS test, Kolmogorov-Smirnov Testi	Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi	KS two-sample test, two-sample KS test, İki Örneklem Kolmogorov-Smirnov Testi
ذات صلة	2	5	3
الملخص	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.	The two-sample Kolmogorov-Smirnov test is a nonparametric procedure that asks whether two independent groups are drawn from the same continuous distribution. Building on Smirnov's 1948 tables, it compares the empirical cumulative distribution functions (CDFs) of the two samples and uses their maximum absolute distance as the test statistic.