$\alpha$-divergence derived as the generalized rate function in a power-law system
| Autor: | Suyari, Hiroki, Scarfone, Antonio Maria |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 5 pages |
| Databáze: | arXiv |
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