  Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein
and Fermi-Dirac statistics, with unequal source probabilities $q_i$ for each
level $i$, are obtained by combinatorial reasoning. For equiprobable degenerate
sublevels, these reduce to those given by Brillouin in 1930, more commonly
given as a statistical weight for each statistic. These distributions and
corresponding cross-entropy (divergence) functions are shown to be special
cases of the P\'olya urn model, involving neither independent nor identically
distributed ("ninid") sampling. The most probable P\'olya distribution contains
the Acharya-Swamy intermediate statistic.
