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 If one or more parameters must be estimated from the sample then the tables are no longer valid.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 an exponential population when the mean is not specified but must be estimated from the sample. The table is obtained from a Monte Carlo calculation.
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Hubert W. Lilliefors (1969) studied this question.
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