A multidimensional version of the Kolmogorov-Smirnov test

The authors discuss a generalization of the classical Kolmogorov-Smirnov test, which is suitable to analyse random samples defined in two or three dimensions. This test provides some improvements with respect to an earlier version proposed by Peacock. Supported by a large number of Monte Carlo simulations, the authors are ensured that this test is sufficiently distribution-free for any practical purposes. They also give a simple analytic expression to make easier the calculation of the critical values of the test probability distribution. To illustrate how the test works, the authors use it to analyse models of the cosmological evolution of X-ray selected active galactic nuclei and they show that it is a much more sensitive goodness-of-fit test than the χ².