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Entropy 2014, 16(10), 5377-5399; doi:10.3390/e16105377

On Some Properties of Tsallis Hypoentropies and Hypodivergences

1
Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan
2
Faculty of Engineering Sciences, LUMINA - University of South-East Europe, ¸ Sos. Colentina 64b, Bucharest, RO-021187, Romania
3
Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85071 Eichstätt, Germany
*
Author to whom correspondence should be addressed.
Received: 15 September 2014 / Accepted: 8 October 2014 / Published: 15 October 2014
(This article belongs to the Section Statistical Mechanics)
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Abstract

Both the Kullback–Leibler and the Tsallis divergence have a strong limitation: if the value zero appears in probability distributions (p1, ··· , pn) and (q1, ··· , qn), it must appear in the same positions for the sake of significance. In order to avoid that limitation in the framework of Shannon statistics, Ferreri introduced in 1980 hypoentropy: “such conditions rarely occur in practice”. The aim of the present paper is to extend Ferreri’s hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties, like nonnegativity, monotonicity, the chain rule and subadditivity, are established. View Full-Text
Keywords: mathematical inequality; Tsallis entropy; Tsallis hypoentropy; Tsallishypodivergence; chain rule; subadditivity mathematical inequality; Tsallis entropy; Tsallis hypoentropy; Tsallishypodivergence; chain rule; subadditivity
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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MDPI and ACS Style

Furuichi, S.; Mitroi-Symeonidis, F.-C.; Symeonidis, E. On Some Properties of Tsallis Hypoentropies and Hypodivergences. Entropy 2014, 16, 5377-5399.

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