A note on some information-theoretic divergences between Zeta distributions

TL;DR

This paper explores the properties of zeta distributions, a class of discrete power law distributions related to Pareto, focusing on their information-theoretic divergences and geometric structure.

Contribution

It provides a detailed analysis of information-theoretic measures and the geometric properties of zeta distributions, a less-studied class of discrete power law distributions.

Findings

Derived expressions for divergences between zeta distributions

Analyzed the information geometry of the zeta distribution family

Identified key properties of zeta distributions in the context of information theory

Abstract

We consider the zeta distributions which are discrete power law distributions that can be interpreted as the counterparts of the continuous Pareto distributions with unit scale. The family of zeta distributions forms a discrete exponential family with normalizing constants expressed using the Riemann zeta function. We report several information-theoretic measures between zeta distributions and study their underlying information geometry.