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 (PDF) of the large-scale density field rho, motivated by a Lagrangian versio n of the continuity equation. It consists in applying the Edgeworth ex pansion to the quantity Phi = log rho - [log rho]. The method is teste d on the matter particle distribution in two cold dark matter N-body s imulations of different physical sizes to cover a large dynamic range. It is seen to be very efficient, even in the nonlinear regime, and ma y thus be used as an analytical tool to study the effect on the PDF of the transition between the weakly nonlinear regime and the highly non linear regime.