The Elliptical Quartic Exponential Distribution: An Annular Distribution Obtained via Maximum Entropy

TL;DR

This paper introduces the Elliptical Quartic Exponential distribution in multidimensional space, derived through maximum entropy principles with specific moment constraints, and provides analytical expressions for its properties.

Contribution

It presents a novel elliptical distribution constructed via maximum entropy with second and fourth moment constraints, including detailed analytical expressions and relationships to existing distributions.

Findings

Derived the distribution using maximum entropy with moment constraints

Provided analytical formulas for normalization constant and entropy

Explored relationships to related elliptical distributions

Abstract

This paper describes the Elliptical Quartic Exponential distribution in $\mathbb{R}^D$, obtained via a maximum entropy construction by imposing second and fourth moment constraints. I discuss relationships to related work, analytical expressions for the normalization constant and the entropy, and the conditional and marginal distributions.