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Open AccessArticle

The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables

Department of Mathematics and Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada
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Entropy 2019, 21(10), 921; https://doi.org/10.3390/e21100921
Received: 19 July 2019 / Revised: 9 September 2019 / Accepted: 16 September 2019 / Published: 22 September 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
The sampling distribution of the total correlation (TC) for a d-dimensional standardized multivariate Gaussian random variable with an identity covariance matrix is derived. It is shown to be the distribution of a sum of generalized beta random variables. It is also shown that, for large dimension and sample size, a central limit theorem holds, providing a Gaussian approximation to the sampling distribution for high dimensional data. View Full-Text
Keywords: mutual information; total correlation; multiinformation; sampling distribution; central limit theorem; multivariate mutual information mutual information; total correlation; multiinformation; sampling distribution; central limit theorem; multivariate mutual information
MDPI and ACS Style

Rowe, T.; Day, T. The Sampling Distribution of the Total Correlation for Multivariate Gaussian Random Variables. Entropy 2019, 21, 921.

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