On Conditional Tsallis Entropy

There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α&...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Andreia Teixeira [verfasserIn] André Souto [verfasserIn] Luís Antunes [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Tsallis entropy conditional Tsallis entropies Generalizations of Shannon entropy

Übergeordnetes Werk:	In: Entropy - MDPI AG, 2003, 23(2021), 11, p 1427
Übergeordnetes Werk:	volume:23 ; year:2021 ; number:11, p 1427

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/e23111427

Katalog-ID:	DOAJ085538566

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language	English
source	In Entropy 23(2021), 11, p 1427 volume:23 year:2021 number:11, p 1427
sourceStr	In Entropy 23(2021), 11, p 1427 volume:23 year:2021 number:11, p 1427
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topic_facet	Tsallis entropy conditional Tsallis entropies Generalizations of Shannon entropy Science Q Astrophysics Physics
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container_title	Entropy
authorswithroles_txt_mv	Andreia Teixeira @@aut@@ André Souto @@aut@@ Luís Antunes @@aut@@
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callnumber-first	Q - Science
author	Andreia Teixeira
spellingShingle	Andreia Teixeira misc QB460-466 misc QC1-999 misc Tsallis entropy misc conditional Tsallis entropies misc Generalizations of Shannon entropy misc Science misc Q misc Astrophysics misc Physics On Conditional Tsallis Entropy
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topic_title	QB460-466 QC1-999 On Conditional Tsallis Entropy Tsallis entropy conditional Tsallis entropies Generalizations of Shannon entropy
topic	misc QB460-466 misc QC1-999 misc Tsallis entropy misc conditional Tsallis entropies misc Generalizations of Shannon entropy misc Science misc Q misc Astrophysics misc Physics
topic_unstemmed	misc QB460-466 misc QC1-999 misc Tsallis entropy misc conditional Tsallis entropies misc Generalizations of Shannon entropy misc Science misc Q misc Astrophysics misc Physics
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title	On Conditional Tsallis Entropy
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title_full	On Conditional Tsallis Entropy
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title_sort	on conditional tsallis entropy
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title_auth	On Conditional Tsallis Entropy
abstract	There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< that converges to the Shannon entropy as <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature—their properties are studied and their values, as a function of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<.
abstractGer	There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< that converges to the Shannon entropy as <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature—their properties are studied and their values, as a function of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<.
abstract_unstemmed	There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< that converges to the Shannon entropy as <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula< approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature—their properties are studied and their values, as a function of <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mi<α</mi<</semantics<</math<</inline-formula<.
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