Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 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.

Original languageEnglish (US)
Pages (from-to)42-62
Number of pages21
JournalScandinavian Journal of Statistics
Volume40
Issue number1
DOIs
StatePublished - Mar 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Arellano-Valle's research was partially supported by grant FONDECYT 1085241-Chile. Contreras-Reyes's research was partially supported by a grant from the Inter-American Institute for Global Change Research (IAI) CRN II 2017, which is supported by the US National Science Foundation (Grant GEO-0452325). Genton's research was partially supported by NSF grant DMS-1007504. This publication is based in part on work supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). The authors thank the editor, an associate editor, a referee and Zdenek Hlavka for their helpful comments and suggestions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Keywords

  • Elliptical distribution
  • Entropy
  • Information theory
  • Optimal network design
  • Shannon
  • Skew-normal
  • Skew-t

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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