  The one-point probability distribution function (pdf) of the large-scale
density field is an important tool to follow the evolution of cosmological
structures. In this paper we present a new model for this pdf for all regimes
and all densities, that is from linear to highly non-linear scales and from
rare voids up to rare high densities. This is probably the simplest model one
can build which is consistent with normalization constraints and known rigorous
results (the quasi-linear regime and the rare void limit). It is fully
parameterized by the non-linear variance and skewness. We obtain a good
agreement with N-body data from realistic cosmological simulations of the VIRGO
consortium and we find that it works significantly better than previous models
such as the lognormal model or the Extended Perturbation Theory (EPT). We
explain this success as a result of the tight constraints onto the pdf provided
by these consistency conditions. We also point out that while the Lagrangian
dynamics of typical fluctuations is quite complex the statistical outcome seems
rather simple. This simple model should be useful for studies which require a
realistic and convenient description of this pdf.
