A closed-form expression for the Sharma-Mittal entropy of exponential families
Information Theory
2021-04-29 v1 math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.1112.4221,
title = {A closed-form expression for the Sharma-Mittal entropy of exponential families},
author = {Frank Nielsen and Richard Nock},
journal= {arXiv preprint arXiv:1112.4221},
year = {2021}
}
Comments
9 pages, 3 figures; Journal of Physics A: Mathematical and Theoretical, December 2011. IOP