# On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown

@article{Lilliefors1967OnTK,
title={On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown},
author={Hubert W. Lilliefors},
journal={Journal of the American Statistical Association},
year={1967},
volume={62},
pages={399-402}
}
• H. Lilliefors
• Published 1 June 1967
• Mathematics
• Journal of the American Statistical Association
Abstract The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely-specified continuous distribution. If one or more parameters must be estimated from the sample then the tables are no longer valid. A table is given in this note for use with the Kolmogorov-Smirnov statistic for testing whether a set of observations is from a normal population when the mean and variance are not specified but must be estimated from the…
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## References

SHOWING 1-5 OF 5 REFERENCES
The Kolmogorov-Smirnov Test for Goodness of Fit
Abstract The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted.
The Use of Maximum Likelihood Estimates in {\chi^2} Tests for Goodness of Fit
• Mathematics
• 1954
The usual test that a sample comes from a distribution of given form is performed by counting the number of observations falling into specified cells and applying the χ2 test to these frequencies. In