Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions |
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Authors: | REINALDO B ARELLANO‐VALLE JAVIER E CONTRERAS‐REYES MARC G GENTON |
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Institution: | 1. Departamento de Estadística, Pontificia Universidad Católica de Chile;2. Departamento de Ingeniería Matemática, Universidad de Chile;3. Department of Statistics, Texas A&M University |
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Abstract: | 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. |
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Keywords: | elliptical distribution entropy information theory optimal network design Shannon skew‐normal skew‐t |
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