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

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.