论文标题
通过连续混合物表征Zeta分布
Characterizing the Zeta Distribution via Continuous Mixtures
论文作者
论文摘要
我们提供了ZETA分布的两个新颖特征：首先，作为负二项式分布的可拖动连续混合物（具有固定形状参数，r> 0）和第二，作为泊松分布的可拖动连续混合物。在R> = 1和泊松情况的负二项式情况下，所得的Zeta分布都是可识别的，因为每种混合物都可以与唯一的混合分布相关联。在0 <r <1的负二项式情况下，混合分布是准分布（对于该分布，准概率密度函数假定了一些负值）。
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).
