On Rényi and Tsallis entropies and divergences for exponential families

Details On Rényi and Tsallis entropies and divergences for exponential families On Rényi and Tsallis entropies and divergences for exponential families

2011-05-17

arxiv.org/abs/1105.3259v1

Journal of Physics A: Mathematical and Theoretical, Volume 45 Number 3, 2012

Computer Science

Information Theory

7 pages

Scientific paper

10.1088/1751-8113/45/3/032003

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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