  The distribution of matter in the universe is, to first order, lognormal.
Improving this approximation requires characterization of the third moment
(skewness) of the log density field. Thus, using Millennium Simulation
phenomenology and building on previous work, we present analytic fits for the
mean, variance, and skewness of the log density field $A$. We further show that
a Generalized Extreme Value (GEV) distribution accurately models $A$; we submit
that this GEV behavior is the result of strong intrapixel correlations, without
which the smoothed distribution would tend (by the Central Limit Theorem)
toward a Gaussian. Our GEV model yields cumulative distribution functions
accurate to within 1.7 per cent for near-concordance cosmologies, over a range
of redshifts and smoothing scales.
