A ``Skewed'' lognormal approximation to the probability distribution function of the large-scale density field

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.