Coverage and large scale anisotropies estimation methods for the Pierre Auger Observatory

When searching for anisotropies in the arrival directions of Ultra High Energy Cosmic Rays, one must estimate the number of events expected in each direction of the sky in the case of a perfect isotropy. We present in this article a new method, developed for the Auger Observatory, based on a smooth estimate of the zenith angle distribution obtained from the data itself (which is essentially unchanged in the case of the presence of a large scale anisotropy pattern). We also study the sensitivity of several methods to detect large-scale anisotropies in the cosmic ray arrival direction distribution : Rayleigh analysis, dipole fitting and angular power spectrum estimation