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On R\'enyi and Tsallis entropies and divergences for exponential families
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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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Cited by 2 Pith papers
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Towards Tsallis Fully Probabilistic Design
Tsallis FPD generalizes standard fully probabilistic design using Tsallis divergence and proves that a double backwards induction fixed-point iteration converges to an optimal solution.
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Non-Parametric Goodness-of-Fit Tests Using Tsallis Entropy Measures
The paper proposes Tsallis-entropy goodness-of-fit tests for q-Gaussian data, but the test statistics are under-defined and the advertised iterative shape-parameter estimator is absent.
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