標題: | The Ordering of Shannon Entropies for the Multivariate Distributions and Distributions of Eigenvalues |
作者: | Tsai, Ming-Tien Hsu, Feng-Ju Tsai, Chia-Hsuan 統計學研究所 Institute of Statistics |
關鍵字: | central Wishart and central MANOVA models;MTP;(2);noncentral Wishart and noncentral MANOVA models |
公開日期: | 1-二月-2019 |
摘要: | 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 (MTP2) 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. |
URI: | http://dx.doi.org/10.3390/e21020201 http://hdl.handle.net/11536/148984 |
ISSN: | 1099-4300 |
DOI: | 10.3390/e21020201 |
期刊: | ENTROPY |
Volume: | 21 |
顯示於類別: | 期刊論文 |