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→The Kolmogorov–Smirnov statistic in more than one dimension 多个维度的Kolmogorov–Smirnov统计
The Kolmogorov–Smirnov test statistic needs to be modified if a similar test is to be applied to [[multivariate statistics|multivariate data]]. This is not straightforward because the maximum difference between two joint [[cumulative distribution function]]s is not generally the same as the maximum difference of any of the complementary distribution functions. Thus the maximum difference will differ depending on which of <math>\Pr(x < X \land y < Y)</math> or <math>\Pr(X < x \land Y > y)</math> or any of the other two possible arrangements is used. One might require that the result of the test used should not depend on which choice is made.
The Kolmogorov–Smirnov test statistic needs to be modified if a similar test is to be applied to [[multivariate statistics|multivariate data]]. This is not straightforward because the maximum difference between two joint [[cumulative distribution function]]s is not generally the same as the maximum difference of any of the complementary distribution functions. Thus the maximum difference will differ depending on which of <math>\Pr(x < X \land y < Y)</math> or <math>\Pr(X < x \land Y > y)</math> or any of the other two possible arrangements is used. One might require that the result of the test used should not depend on which choice is made.
如果要将类似的检验应用于多元数据，则需要修改Kolmogorov–Smirnov检验统计量。过程略显复杂，因为两个联合累积分布函数之间的最大差异通常与任何互补分布函数中的最大差异都不相同。因此，最大差异将取决于使用<math>\Pr(x < X \land y < Y)</math>或<math>\Pr(X < x \land Y > y)</math>中的哪一个，或者使用其他两种可能分布中的任何一种。当然也有可能要求所用的检测结果无关于使用选择。