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One approach to generalizing the Kolmogorov–Smirnov statistic to higher dimensions which meets the above concern is to compare the cdfs of the two samples with all possible orderings, and take the largest of the set of resulting K–S statistics.  In ''d'' dimensions, there are 2^''d''−1 such orderings.  One such variation is due to Peacock(see also Gosset for a 3D version) and another to Fasano and Franceschini (see Lopes et al. for a comparison and computational details). Critical values for the test statistic can be obtained by simulations, but depend on the dependence structure in the joint distribution.

One approach to generalizing the Kolmogorov–Smirnov statistic to higher dimensions which meets the above concern is to compare the cdfs of the two samples with all possible orderings, and take the largest of the set of resulting K–S statistics.  In ''d'' dimensions, there are 2^''d''−1 such orderings.  One such variation is due to Peacock(see also Gosset for a 3D version) and another to Fasano and Franceschini (see Lopes et al. for a comparison and computational details). Critical values for the test statistic can be obtained by simulations, but depend on the dependence structure in the joint distribution.

在满足以上要求的同时，将Kolmogorov-Smirnov统计量泛化为更高维度的一种方法是，比较两个样本的累积分布函数与所有可能的排序，并从所得的K-S统计量集中最大。在d维中，有2d-1个这样的排序。Peacock得出了一种这样的变化量（有关3D版本，另请参见Gosset），另一种由Fasano和Franceschini得出（有关比较和计算细节，请参见Lopes等人）。可以通过模拟获得检测统计量的临界值，但取决于联合分布中的依存关系的结构。

在满足以上要求的同时，将Kolmogorov-Smirnov统计量泛化为更高维度的一种方法是，比较两个样本的累积分布函数与所有可能的排序，并从所得的K-S统计量集中最大。在d维中，有2d-1个这样的排序。Peacock得出了一种这样的变化量（有关3D版本，另请参见Gosset），另一种由Fasano和Franceschini得出（有关比较和计算细节，请参见Lopes等人）。可以通过模拟获得检测统计量的临界值，但取决于联合分布中的依存关系结构。