A closed-form expression for the Sharma-Mittal entropy of exponential families
نویسندگان
چکیده
The Sharma-Mittal entropies generalize the celebrated Shannon, Rényi and Tsallis entropies. We report a closed-form formula for the Sharma-Mittal entropies and relative entropies for arbitrary exponential family distributions. We instantiate explicitly the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. PACS numbers: 03.65.Ta, 03.67.-a Submitted to: Journal of Physics A: Mathematical and Theoretical Fast Track Communications (revised manuscript, Nov. 2011; accepted Nov. 2011) A closed-form expression for the Sharma-Mittal entropy of exponential families 2 The Sharma-Mittal entropy Hα,β(p) [1, 2] of a probability density‡ p is defined as Hα,β(p) = 1 1− β
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FAST TRACK COMMUNICATION A closed-form expression for the Sharma–Mittal entropy of exponential families
The Sharma–Mittal entropies generalize the celebrated Shannon, Rényi and Tsallis entropies. We report a closed-form formula for the Sharma–Mittal entropies and relative entropies for arbitrary exponential family distributions. We explicitly instantiate the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. Q1 Q2 PACS numbers: 03.65.Ta, 03.67.−a (Some ...
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ورودعنوان ژورنال:
- CoRR
دوره abs/1112.4221 شماره
صفحات -
تاریخ انتشار 2011