通过连续混合物表征Zeta分布
Characterizing the Zeta Distribution via Continuous Mixtures
摘要：
我们提供了两个新的Zeta分布的特征：第一，作为一个易于处理的连续混合的负二项分布（与固定的形状参数，r > 0），第二，作为一个易于处理的连续混合的泊松分布。在r >= 1的负二项情况和泊松情况下，所得到的Zeta分布是可识别的，因为每个混合物可以与唯一的混合分布相关联。在0 < r < 1的负二项分布情况下，混合分布是准分布（准密度函数假定某些负值）。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
