مقایسهٔ روش‌ها

	تخمین چگالی کرنل و آزمون توزیع (KDE)	آزمون لیلیفورس برای نرمال بودن
حوزه	آمار	آمار
خانواده	Regression model	Regression model
سال پیدایش	1956	1967
پدیدآور	Rosenblatt (1956); Parzen (1962); textbook treatment by Silverman	Hubert W. Lilliefors
نوع	Nonparametric density estimation	Goodness-of-fit / normality test
منبع بنیادین	Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function. Annals of Mathematical Statistics, 27(3), 832-837.	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.
نام‌های دیگر	kernel density estimate, KDE, Parzen window estimation, nonparametric density estimation	Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi
مرتبط	4	5
خلاصه	Kernel Density Estimation is a nonparametric method that estimates a continuous probability density by placing a smooth kernel function over each observation, without assuming any parametric distribution. It traces back to Rosenblatt (1956) and the textbook treatment by Silverman (1986), and it also supports distribution-comparison tests built on the estimated densities.	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.