标题： Zeta尾分布：一种新的事件计数模型 显示英文标题

标题： The Zeta Tail Distribution: A Novel Event-Count Model

摘要： 我们引入了Zeta Tail(a)概率分布作为一种新的模型，用于风险分析中的随机损坏事件计数。 尽管作为几何分布Geometric(p)的类比而容易被提出，但Zeta Tail(a)在学术文献中受到的关注很少。 在本研究中，我们首先推导了这种新分布的各种基本性质。 然后，我们通过理论分析和对一组气象数据的应用来评估其作为Geometric(p)替代模型的实用性。 最后，我们讨论了在条件（即，给定具有某些已知特征的观测数据）下使用Zeta Tail(a)模型与在无条件（即，对于任意尚未观测的数据）下使用该模型之间的概念性差异。 显示英文摘要

摘要： We introduce the Zeta Tail(a) probability distribution as a new model for random damage-event counts in risk analysis. Although readily motivated as an analogue of the Geometric(p) distribution, Zeta Tail(a) has received little attention in the scholarly literature. In the present work, we begin by deriving various fundamental properties of this novel distribution. We then assess its usefulness as an alternative to Geometric(p), both theoretically and through application to a set of meteorological data. Lastly, we discuss conceptual differences between employing the Zeta Tail(a) model conditionally (i.e., given observed data with certain known characteristics) and unconditionally (i.e., for arbitrary, as yet unobserved data).