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

Marina Muniz; Roger Silva; Rosangela Loschi

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

Statistics Theory 2016-09-21 v2 Statistics Theory

Authors: Marina Muniz , Roger Silva , Rosangela Loschi

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.

Keywords

Shannon entropy Kullback-Leibler divergence multivariate log canonical fundamental skew-normal canonical fundamental skew-normal mutual information model comparison clustering

Cite

@article{arxiv.1408.4755,
  title  = {Shannon Entropy and Kullback-Leibler Divergence in Multivariate Log Fundamental Skew-Normal and Related Distributions},
  author = {Marina Muniz and Roger Silva and Rosangela Loschi},
  journal= {arXiv preprint arXiv:1408.4755},
  year   = {2016}
}

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21 pages

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

Abstract

Keywords

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