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

Frank Nielsen; Richard Nock

doi:10.1088/1751-8113/45/3/032003

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

Frank Nielsen^*, Richard Nock

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

59 Citations (Scopus)

Abstract

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 its estimation.

Original language	English
Article number	032003
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	45
Issue number	3
DOIs	https://doi.org/10.1088/1751-8113/45/3/032003
Publication status	Published - 27 Jan 2012
Externally published	Yes

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abstract = "The Sharma-Mittal entropies generalize the celebrated Shannon, R{\'e}nyi 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 its estimation.",

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AB - 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 its estimation.

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

Abstract

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