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| Lilliefors 正态性检验× | 双样本柯尔莫哥洛夫-斯米尔诺夫检验× | |
|---|---|---|
| 领域 | 统计学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1967 | 1948 |
| 提出者≠ | Hubert W. Lilliefors | N. V. Smirnov |
| 类型≠ | Goodness-of-fit / normality test | Nonparametric two-sample distribution test |
| 开创性文献≠ | 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. DOI ↗ | Smirnov, N. V. (1948). Table for Estimating the Goodness of Fit of Empirical Distributions. Annals of Mathematical Statistics, 19(2), 279-281. DOI ↗ |
| 别名 | Lilliefors corrected Kolmogorov-Smirnov test, Lilliefors normality test, Lilliefors Testi | KS two-sample test, two-sample KS test, İki Örneklem Kolmogorov-Smirnov Testi |
| 相关≠ | 5 | 3 |
| 摘要≠ | 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. |
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