  We use the physics of ellipsoidal collapse to model the probability
distribution function of the smoothed dark matter density field in real and
redshift space. We provide a simple approximation to the exact collapse model
which shows clearly how the evolution can be thought of as a modification of
the spherical evolution model as well as of the Zeldovich Approximation. In
essence, our model specifies how the initial smoothed overdensity and shear
fields can be used to determine the shape and size of the region at later
times. We use our parametrization to extend previous work on the real-space PDF
so that it predicts the redshift space PDF as well. Our results are in good
agreement with measurements of the PDF in simulations of clustering from
Gaussian initial conditions down to scales on which the rms fluctuation is
slightly greater than unity. We also show how the highly non-Gaussian
non-linear redshifted density field in a numerical simulation can be
transformed so that it provides an estimate of the shape of the initial
real-space PDF. When applied to our simulations, our method recovers the
initial Gaussian PDF, provided the variance in the nonlinear smoothed field is
less than 4.
