On Some Properties of Tsallis Hypoentropies and Hypodivergences
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. MSC classifications: 26D15; 94A17
- Publication:
-
Entropy
- Pub Date:
- October 2014
- DOI:
- 10.3390/e16105377
- arXiv:
- arXiv:1410.4903
- Bibcode:
- 2014Entrp..16.5377F
- Keywords:
-
- mathematical inequality;
- Tsallis entropy;
- Tsallis hypoentropy;
- Tsallis hypodivergence;
- chain rule;
- subadditivity;
- Condensed Matter - Statistical Mechanics;
- 26D15 and 94A17
- E-Print:
- 23 pages