  The search of a clustering signal in the arrival directions of
ultra-high-energy cosmic rays (UHECRs) is a standard method to assess the level
of anisotropy of the data sets under investigation. Here, we first show how to
quantify the sensitivity of a UHECR detector to the detection of anisotropy,
and then propose a new method that pushes forward the study of the two-point
auto-correlation function, enabling one to put astrophysically meaningful
constraints on both the effective UHECR source density and the angular
deflections that these charged particles suffer while they propagate through
the galactic and intergalactic magnetic fields. We apply the method to
simulated data sets obtained under various astrophysical conditions, and show
how the input model parameters can be estimated through our analysis,
introducing the notion of "clustering similarity" (between data sets), to which
we give a precise statistical meaning. We also study how the constraining power
of the method is influenced by the size of the data set under investigation,
the minimum energy of the UHECRs to which it is applied, and a prior assumption
about the underlying source distribution. We also show that this method is
particularly adapted to data sets consisting of a few tens to a few hundreds of
events, which corresponds to the current and near-future observational
situation in the field of UHECRs.
