  Colombi et al. 1999 (paper I) investigated the counts-in-cells statistics and
their respective errors in the $\tau$CDM Virgo Hubble Volume simulation. This
extremely large $N$-body experiment also allows a numerical investigation of
the {\em cosmic distribution function}, $\Upsilon(\tA)$ itself for the first
time. For a statistic $A$, $\Upsilon(\tA)$ is the probability density of
measuring the value $\tA$ in a finite galaxy catalog. $\Upsilon$ was evaluated
for the distribution of counts-in-cells, $P_N$, the factorial moments, $F_k$,
and the cumulants, $\xiav$ and $S_N$'s, using the same subsamples as paper I.
While paper I concentrated on the first two moments of $\Upsilon$, i.e. the
mean, the cosmic error and the cross-correlations, here the function $\Upsilon$
is studied in its full generality, including a preliminary analysis of joint
distributions $\Upsilon(\tA,\tB)$. The most significant, and reassuring result
for the analyses of future galaxy data is that the cosmic distribution function
is nearly Gaussian provided its variance is small. A good practical criterion
for the relative cosmic error is that $\Delta A/A \la 0.2$. This means that for
accurate measurements, the theory of the cosmic errors, presented by Szapudi &
Colombi (1996) and Szapudi, Colombi & Bernardeau (1999), and confirmed
empirically by paper I, is sufficient for a full statistical description and
thus for a maximum likelihood rating of models. As the cosmic error increases,
the cosmic distribution function $\Upsilon$ becomes increasingly skewed and is
well described by a generalization of the lognormal distribution. The cosmic
skewness is introduced as an additional free parameter. (...more in paper...)
