Shannon Entropy and Kullback-Leibler Divergence in Multivariate Log Fundamental Skew-Normal and Related Distributions

TL;DR

This paper derives Shannon entropy and Kullback-Leibler divergence formulas for multivariate skew-normal distributions, relating them to other distributions and applying these measures to climate data analysis.

Contribution

It extends existing entropy and divergence results to multivariate skew-normal families and introduces applications in climate data clustering and model comparison.

Findings

Derived explicit entropy and divergence formulas for skew-normal distributions.

Applied entropy to compare climate models fitted to precipitation data.

Used divergence to cluster Atlantic regions by humidity levels.

Abstract

This paper mainly focuses on studying the Shannon Entropy and Kullback-Leibler divergence of the multivariate log canonical fundamental skew-normal (LCFUSN) and canonical fundamental skew-normal (CFUSN) families of distributions, extending previous works. We relate our results with other well known distributions entropies. As a byproduct, we also obtain the Mutual Information for distributions in these families. Shannon entropy is used to compare models fitted to analyze the USA monthly precipitation data. Kullback-Leibler divergence is used to cluster regions in Atlantic ocean according to their air humidity level.