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

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