A 'skewed' lognormal approximation to the probablility distribution function of the large-scale density field

The author proposes a new method to fit the probability distribution function (PDF) of the large-scale density field ρ, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the quantity Φ ≡ log ρ - >log ρ<. 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 nonlinear regime, and may 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 nonlinear regime.