Shannon entropy and Kullback–Leibler divergence in multivariate log fundamental skew‐normal and related distributions

This article 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 entropies of other well-known distributions. As a by-product we also obtain the mutual information for distributions in these families. Shannon entropy is used to compare models fitted to analyze monthly USA precipitation data. Kullback–Leibler divergence is used to cluster regions in the Atlantic ocean according to their air humidity level. The Canadian Journal of Statistics 44: 219–237; 2016 © 2016 Statistical Society of Canada