  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.
