Kolmogorov-Smirnov test as a tool to study the distribution of ultra-high energy cosmic ray sources

We analyze in detail the two-dimensional Kolmogorov-Smirnov test as a tool to learn about the distribution of the sources of the ultra-high energy cosmic rays. We confront in particular models based on AGN observed in X rays, on galaxies observed in HI and isotropic distributions, discussing how this method can be used not only to reject isotropy but also to support or reject specific source models, extending results obtained recently in the literature.