  Using a suite of self-similar cosmological simulations, we measure the
probability distribution functions (PDFs) of real-space density, redshift-space
density, and their geometric mean. We find that the real-space density PDF is
well-described by a function of two parameters: $n_s$, the spectral slope, and
$\sigma_L$, the linear rms density fluctuation. For redshift-space density and
the geometric mean of real- and redshift-space densities, we introduce a third
parameter, $s_L={\sqrt{\langle(dv^L_{\rm pec}/dr)^2\rangle}}/{H}$. We find that
density PDFs for the LCDM cosmology is also well-parameterized by these three
parameters. As a result, we are able to use a suite of self-similar
cosmological simulations to approximate density PDFs for a range of
cosmologies. We make the density PDFs publicly available and provide an
analytical fitting formula for them.
