The Zeta Tail Distribution: A Novel Event-Count Model

TL;DR

This paper introduces the Zeta Tail distribution as a new model for event-count data in risk analysis, deriving its properties, comparing it to the Geometric distribution, and demonstrating its application to meteorological data.

Contribution

It presents the Zeta Tail distribution as a novel alternative to existing models, with detailed theoretical properties and practical application insights.

Findings

Zeta Tail distribution has distinct properties from Geometric distribution.

Application to meteorological data shows its practical usefulness.

Conceptual analysis of conditional versus unconditional modeling.

Abstract

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).