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alpha-Divergence derived as the generalized rate function in Tsallis statistics (Articolo in rivista)

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alpha-Divergence derived as the generalized rate function in Tsallis statistics (Articolo in rivista) (literal)

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H. Suyari and A.M. Scarfone (2014)
alpha-Divergence derived as the generalized rate function in Tsallis statistics
in IEICE technical report The Institute of Electronics, Information and Communication Engineers
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Graduate School of Advanced Integration Science, Chiba University 1-33 Yayoi, Inage, Chiba 263-8522, Japan Istituto dei Sistemi Complessi (ISC-CNR) c/o Dipartimento di Scienza Applicatae Tecnologia, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy (literal)

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alpha-Divergence derived as the generalized rate function in Tsallis statistics (literal)

Abstract

The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise q-Stirling's formula. The alpha-divergence (or q-divergence) is uniquely derived from the generalized binomial distribution in the sense that when q->-1 (i.e., q->1) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial considerations, it is shown that alpha-divergence (or q-divergence) is appeared as the generalized rate function in the large deviation estimate in Tsallis statistics. (literal)

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