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

Characterizing the Zeta Distribution via Continuous Mixtures