Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions

Reinaldo B. Arellano-Valle, Javier E. Contreras-Reyes, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study in detail the cases of the multivariate skew-normal and skew-t distributions. We implement our findings to the application of the optimal design of an ozone monitoring station network in Santiago de Chile. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.
Original languageEnglish (US)
Pages (from-to)42-62
Number of pages21
JournalScandinavian Journal of Statistics
Volume40
Issue number1
DOIs
StatePublished - Feb 27 2012
Externally publishedYes

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