A closed-form expression for the Sharma-Mittal entropy of exponential families

Details A closed-form expression for the Sharma-Mittal entropy of exponential families A closed-form expression for the Sharma-Mittal entropy of exponential families

2011-12-19

arxiv.org/abs/1112.4221v1

Computer Science

Information Theory

9 pages, 3 figures; Journal of Physics A: Mathematical and Theoretical, December 2011. IOP

Scientific paper

The Sharma-Mittal entropies generalize the celebrated Shannon, R\'enyi 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.

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