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arXiv · 1105.3259

On R\'enyi and Tsallis entropies and divergences for exponential families

Frank Nielsen·Richard Nock
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Abstract

Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both R\'enyi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that R\'enyi and Tsallis entropies can also be calculated in closed-form for sub-families including the Gaussian or exponential distributions, among others.

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Frank Nielsen, Richard Nock. 2011-05-17. On R\'enyi and Tsallis entropies and divergences for exponential families. https://doi.org/10.1088/1751-8113/45/3/032003

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