Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions

DOI10.1111/j.1467-9469.2011.00774.xzbMath1259.62002OpenAlexW1525415266MaRDI QIDQ4911965

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

Publication date: 20 March 2013

Published in: Scandinavian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/134799

zbMATH Keywords

information theoryskew-\(t\)skew-normalelliptical distributionoptimal network design

Mathematics Subject Classification ID

Applications of statistics to environmental and related topics (62P12) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Measures of information, entropy (94A17) Statistical aspects of information-theoretic topics (62B10)

Related Items

Rényi entropy and complexity measure for skew-Gaussian distributions and related families, Mutual information rate between stationary Gaussian processes, Shannon Information Ink-records, Generalized multivariate Birnbaum-Saunders distributions and related inferential issues, A mutual information-basedk-sample test for discrete distributions, Kullback-Leibler divergence measure for multivariate skew-normal distributions, Maximum a-posteriori estimation of autoregressive processes based on finite mixtures of scale-mixtures of skew-normal distributions, Addressing non-normality in multivariate analysis using the \(t\)-distribution, Information quantity evaluation of nonlinear time series processes and applications, Unnamed Item, Robust linear functional mixed models, On dynamic mutual information for bivariate lifetimes, Asymptotic form of the Kullback-Leibler divergence for multivariate asymmetric heavy-tailed distributions, Unique information via dependency constraints, Bayesian multivariate sparse functional principal components analysis with application to longitudinal microbiome multiomics data, Shannon entropy and Kullback–Leibler divergence in multivariate log fundamental skew‐normal and related distributions, A broad class of multivariate distributions for rates and proportions, Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

Uses Software

• R
• sn

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• Multivariate extended skew-\(t\) distributions and related families
• On the information matrix of the multivariate skew-\(t\) model
• An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators
• Estimation of the entropy of a multivariate normal distribution
• On some characterizations of the \(t\)-distribution
• On fundamental skew distributions
• Bayesian inference in spherical linear models: robustness and conjugate analysis
• Perturbation of Numerical Confidential Data via Skew-t Distributions
• On the Unification of Families of Skew-normal Distributions
• Entropy expressions and their estimators for multivariate distributions
• Statistical Applications of the Multivariate Skew Normal Distribution
• The multivariate skew-normal distribution
• Multivariate skewt-distribution
• Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skewt-Distribution
• Flexible Class of Skew-Symmetric Distributions
• Elements of Information Theory
• A general class of multivariate skew-elliptical distributions