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$α$-divergence derived as the generalized rate function in a power-law system (1405.2562v1)
Published 11 May 2014 in math-ph, cs.IT, math.IT, and math.MP
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 $\alpha\rightarrow-1$ (i.e., $q\rightarrow1$) 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.