  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.
