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&...
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2021
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oai:doaj.org-article:965806f6defb429e9413af8f9c7ff7092021-11-25T17:29:35ZOn Conditional Tsallis Entropy10.3390/e231114271099-4300https://doaj.org/article/965806f6defb429e9413af8f9c7ff7092021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1427https://doaj.org/toc/1099-4300There 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>.Andreia TeixeiraAndré SoutoLuís AntunesMDPI AGarticleTsallis entropyconditional Tsallis entropiesGeneralizations of Shannon entropyScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1427, p 1427 (2021) |
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DOAJ |
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EN |
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Tsallis entropy conditional Tsallis entropies Generalizations of Shannon entropy Science Q Astrophysics QB460-466 Physics QC1-999 |
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Tsallis entropy conditional Tsallis entropies Generalizations of Shannon entropy Science Q Astrophysics QB460-466 Physics QC1-999 Andreia Teixeira André Souto Luís Antunes On Conditional Tsallis Entropy |
| description |
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>. |
| format |
article |
| author |
Andreia Teixeira André Souto Luís Antunes |
| author_facet |
Andreia Teixeira André Souto Luís Antunes |
| author_sort |
Andreia Teixeira |
| title |
On Conditional Tsallis Entropy |
| title_short |
On Conditional Tsallis Entropy |
| title_full |
On Conditional Tsallis Entropy |
| title_fullStr |
On Conditional Tsallis Entropy |
| title_full_unstemmed |
On Conditional Tsallis Entropy |
| title_sort |
on conditional tsallis entropy |
| publisher |
MDPI AG |
| publishDate |
2021 |
| url |
https://doaj.org/article/965806f6defb429e9413af8f9c7ff709 |
| work_keys_str_mv |
AT andreiateixeira onconditionaltsallisentropy AT andresouto onconditionaltsallisentropy AT luisantunes onconditionaltsallisentropy |
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1718412298656153600 |