%0 Journal Article %1 nielsen2011closedform %A Nielsen, Frank %A Nock, Richard %D 2011 %K bayesian divergences entropy %R 10.1088/1751-8113/45/3/032003 %T A closed-form expression for the Sharma-Mittal entropy of exponential families %U http://arxiv.org/abs/1112.4221 %X 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.

@article{nielsen2011closedform, 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.}, added-at = {2019-12-11T14:45:16.000+0100}, author = {Nielsen, Frank and Nock, Richard}, biburl = {https://www.bibsonomy.org/bibtex/2f6c6562f2941390f6d65584b8f353efc/kirk86}, description = {[1112.4221] A closed-form expression for the Sharma-Mittal entropy of exponential families}, doi = {10.1088/1751-8113/45/3/032003}, interhash = {b4d99354e9665352b80a53c2f65ffb7d}, intrahash = {f6c6562f2941390f6d65584b8f353efc}, keywords = {bayesian divergences entropy}, note = {cite arxiv:1112.4221Comment: 9 pages, 3 figures; Journal of Physics A: Mathematical and Theoretical, December 2011. IOP}, timestamp = {2019-12-11T14:45:16.000+0100}, title = {A closed-form expression for the Sharma-Mittal entropy of exponential families}, url = {http://arxiv.org/abs/1112.4221}, year = 2011 }