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Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions
Author(s) -
ARELLANOVALLE REINALDO B.,
CONTRERASREYES JAVIER E.,
GENTON MARC G.
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00774.x
Subject(s) - multivariate statistics , skew , mathematics , mutual information , multivariate analysis , entropy (arrow of time) , multivariate normal distribution , context (archaeology) , statistics , rényi entropy , generalized entropy index , principle of maximum entropy , computer science , geography , physics , telecommunications , quantum mechanics , archaeology , panel data
. 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.