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Tsallis distribution as a standard maximum entropy solution with ‘tail’ constraint

By J. -f. Bercher


We show that Tsallis ’ distributions can be derived from the standard (Shannon) maximum entropy setting, by incorporating a constraint on the divergence between the distribution and another distribution imagined as its tail. In this setting, we find an underlying entropy which is the Rényi entropy. Furthermore, escort distributions and generalized means appear as a direct consequence of the construction. Finally, the “maximum entropy tail distribution ” is identified as a Generalized Pareto Distribution. Key words: Maximum entropy principle, Rényi entropy, nonextensive statistic

Topics: PACS,, 02.50.-r, 05.90.+m
Year: 2008
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