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

**Hubert W. Lilliefors**

CiteWeb id: 20120000083

CiteWeb score: 2980

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 If one or more parameters must be estimated from the sample then the tables are no longer valid.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 sample. The table is obtained from a Monte Carlo calculation. A brief Monte Carlo investigation is made of the power of the test.

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