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If either the form or the parameters of ''F''(''x'') are determined from the data ''X''_''i'' the critical values determined in this way are invalid. In such cases, [[Monte Carlo method|Monte Carlo]] or other methods may be required, but tables have been prepared for some cases. Details for the required modifications to the test statistic and for the critical values for  the [[normal distribution]] and the [[exponential distribution]] have been published, and later publications also include the [[Gumbel distribution]]. The [[Lilliefors test]] represents a special case of this for the normal distribution. The logarithm transformation may help to overcome cases where the Kolmogorov test data does not seem to fit the assumption that it came from the normal distribution.

If either the form or the parameters of ''F''(''x'') are determined from the data ''X''_''i'' the critical values determined in this way are invalid. In such cases, [[Monte Carlo method|Monte Carlo]] or other methods may be required, but tables have been prepared for some cases. Details for the required modifications to the test statistic and for the critical values for  the [[normal distribution]] and the [[exponential distribution]] have been published, and later publications also include the [[Gumbel distribution]]. The [[Lilliefors test]] represents a special case of this for the normal distribution. The logarithm transformation may help to overcome cases where the Kolmogorov test data does not seem to fit the assumption that it came from the normal distribution.

如果以数据Xi来确定F（x）的形式或参数，则以这种方式确定的临界值是无效的。在这种情况下，可能需要Monte Carlo或其他方法，但是数据表格已经做了多个情况背景的准备。目前已经发布了对测试统计量的必要修正细节以及正态分布和指数分布临界值的具体信息，以后的出版物还包括Gumbel分布。另外Lilliefors检测代表正态分布的一种特殊情况。另外为了克服Kolmogorov检验数据疑似不符合来自正态分布假设的情况，可以进行对数变换。

如果以数据Xi来确定F（x）的形式或参数，则以这种方式确定的临界值是无效的。在这种情况下，可能需要Monte Carlo或其他方法，不过数据表格已经做了多个情况背景的准备。目前已经发布了对测试统计量的必要修正细节以及正态分布和指数分布临界值的具体信息，以后的出版物还包括Gumbel分布。另外Lilliefors检测代表正态分布的一种特殊情况。另外为了克服Kolmogorov检验数据疑似不符合来自正态分布假设的情况，可以进行对数变换。