Characterizing the Zeta Distribution via Continuous Mixtures

2020/08/14 by Dai, Jiansheng, Huang, Ziheng, Powers, Michael R. +1 · 1 citation
#60E05 (Primary) #62E10 (Secondary) #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2008.06200

Abstract

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).

Cited by

• Assessing Risk Heterogeneity through Heavy-Tailed Frequency and Severity Mixtures

Related

• A note on some information-theoretic divergences between Zeta distributions
• Asymptotic tail properties of Poisson mixture distributions
• Mixed Poisson families with real-valued mixing distributions
• Continuous scaled phase-type distributions
• A new non-negative distribution with both finite and infinite support