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Keywords = Tsallis hypodivergence

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23 pages, 278 KB  
Article
On Some Properties of Tsallis Hypoentropies and Hypodivergences
by Shigeru Furuichi, Flavia-Corina Mitroi-Symeonidis and Eleutherius Symeonidis
Entropy 2014, 16(10), 5377-5399; https://doi.org/10.3390/e16105377 - 15 Oct 2014
Cited by 11 | Viewed by 6584
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 [...] Read more.
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. Full article
(This article belongs to the Section Statistical Physics)
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