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.
alpha-Divergence derived as the generalized rate function in Tsallis statistics
A. M. Scarfone
2014
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.File in questo prodotto:
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Descrizione: alpha -divergence derived as the generalized rate function in Tsallis statistics
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