  I propose a method to fit the probability distribution function (hereafter
PDF) of the large scale density field rho, motivated by a Lagrangian version of
the continuity equation. It consists in applying the Edgeworth expansion to the
quantity Phi=log rho - < log rho >. The method is tested on the matter particle
distribution in two cold dark matter N-body simulations of different physical
sizes to cover a large dynamic range. It is seen to be very efficient, even in
the non-linear regime, and may thus be used as an analytical tool to study the
effect on the PDF of the transition between the weakly non-linear regime and
the highly non-linear regime.
