  We offer two novel characterizations of the Zeta distribution: first, as
tractable continuous mixtures of Negative Binomial distributions (with fixed
shape parameter, r > 0), and second, as a tractable continuous mixture of
Poisson distributions. In both the Negative Binomial case for r >= 1 and the
Poisson case, the resulting Zeta distributions are identifiable because each
mixture can be associated with a unique mixing distribution. In the Negative
Binomial case for 0 < r < 1, the mixing distributions are quasi-distributions
(for which the quasi-probability density function assumes some negative
values).
