The Case for Shifting the Rényi Entropy
Department of Signal Theory and Communications, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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Author to whom correspondence should be addressed.
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These authors contributed equally to this work.
Entropy 2019, 21(1), 46; https://doi.org/10.3390/e21010046
Received: 15 November 2018
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Revised: 1 January 2019
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Accepted: 7 January 2019
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Published: 9 January 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi entropy to quantities close to it, like the information potential and the partition function of statistical mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi entropy is fruitful in some applications.
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Keywords:
shifted Rényi entropy; Shannon-type relations; generalized weighted means; Hölder means; escort distributions
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MDPI and ACS Style
Valverde-Albacete, F.J.; Peláez-Moreno, C. The Case for Shifting the Rényi Entropy. Entropy 2019, 21, 46. https://doi.org/10.3390/e21010046
AMA Style
Valverde-Albacete FJ, Peláez-Moreno C. The Case for Shifting the Rényi Entropy. Entropy. 2019; 21(1):46. https://doi.org/10.3390/e21010046
Chicago/Turabian StyleValverde-Albacete, Francisco J., and Carmen Peláez-Moreno. 2019. "The Case for Shifting the Rényi Entropy" Entropy 21, no. 1: 46. https://doi.org/10.3390/e21010046
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