A three-dimensional extended Kolmogorov-Smirnov test as a useful tool in astronomy

The authors derive a three-dimensional version of the well-known Kolmogorov-Smirnov test. Such a test is of great practical interest when one wishes to investigate the spatial distribution of a set of data points, particularly for the case of small size samples. A comparison with assumed three-dimensional density laws is made possible for most of current applications. A table of critical values of the new statistic is given for usual significance levels; empirical formulate to simulate the asymptotic behaviour are given as well. The tree-dimensional extended two-sided Kolmogorov-Smirnov test is shown to be sufficiently distribution-free.