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 Rényi
and Tsallis divergences of distributions belonging to the same exponential
family admit a generic closed form expression. Furthermore, we show that
Rényi 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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