Kullback-Leibler divergence for the Fr\'echet extreme-value distribution

TL;DR

This paper derives a simple closed-form expression for the Kullback-Leibler divergence between two Fréchet extreme-value distributions, involving fundamental constants, which facilitates analysis and comparison of such distributions.

Contribution

The paper provides the first explicit closed-form formula for the KL divergence between two Fréchet distributions, simplifying divergence calculations in extreme-value analysis.

Findings

Closed-form KL divergence involving Euler-Mascheroni constant

Simplifies divergence computation for Fréchet distributions

Facilitates statistical analysis of extreme-value models

Abstract

We derive a closed-form solution for the Kullback-Leibler divergence between two Fr\'echet extreme-value distributions. The resulting expression is rather simple and involves the Euler-Mascheroni constant.