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Entropy 2019, 21(2), 201; https://doi.org/10.3390/e21020201

The Ordering of Shannon Entropies for the Multivariate Distributions and Distributions of Eigenvalues

1
Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan
2
Center for General Education, Saint Mary’s Junior College of Medicine, Nursing and Management, Yi-Lang 266, Taiwan
3
Institute of Statistics, National Chiao-Tung University, Hsin-Chu 30010, Taiwan
*
Author to whom correspondence should be addressed.
Received: 14 January 2019 / Revised: 17 February 2019 / Accepted: 18 February 2019 / Published: 20 February 2019
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Abstract

In this paper, we prove the Shannon entropy inequalities for the multivariate distributions via the notion of convex ordering of two multivariate distributions. We further characterize the multivariate totally positive of order 2 ( M T P 2 ) property of the distribution functions of eigenvalues of both central Wishart and central MANOVA models, and of both noncentral Wishart and noncentral MANOVA models under the general population covariance matrix set-up. These results can be directly applied to both the comparisons of two Shannon entropy measures and the power monotonicity problem for the MANOVA problem. View Full-Text
Keywords: central Wishart and central MANOVA models; MTP2; noncentral Wishart and noncentral MANOVA models central Wishart and central MANOVA models; MTP2; noncentral Wishart and noncentral MANOVA models
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tsai, M.-T.; Hsu, F.-J.; Tsai, C.-H. The Ordering of Shannon Entropies for the Multivariate Distributions and Distributions of Eigenvalues. Entropy 2019, 21, 201.

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