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).

翻译：我们对Zeta分布提供两种新的特征描述:第一,作为负二氧化物分布(有固定形状参数,r > 0)的可移植连续混合物;第二,作为Poisson分布的可移动连续混合物。在 r & 1 和 Poisson 的负二氧化物案例中,所产生的Zeta分布是可以识别的,因为每种混合物都可能与独特的混合分布有关。在 0 < r < 1 的负二氧化物案例中,混合分布是准分布(准概率密度函数假定某些负值)。