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 If one or more parameters must be estimated from the sample then the tables are no longer valid.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
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…
Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size
On Tests of Normality and Other Tests of Goodness of Fit Based on Distance Methods
The probability integral transformation when parameters are estimated from the sample.