TSALLIS' ENTROPIES - AXIOMATICS, ASSOCIATED f-DIVERGENCES AND FISHER'S INFORMATION

Tertius de Wet; Ferdinand OEsterreicher; Maximilian Thaler

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TSALLIS' ENTROPIES - AXIOMATICS, ASSOCIATED f-DIVERGENCES AND FISHER'S INFORMATION

机译：Tsallis'extopies - 公理，相关的F分歧和Fisher的信息

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In a previous paper, de Wet and OEsterreicher (2016) showed how Arimoto's extended class of entropies generates a family of f-divergences leading to approximation results and finally to Fisher's information in a limiting way. In the current paper, the so-called Tsallis class of entropies is used in a similar fashion to generate a new family of f-divergences with analogous properties. The approximation properties are proved in a form which significantly generalizes the corresponding results in the above mentioned paper.

机译：在之前的论文中，De Wet和Oesterreicher（2016年）显示Arimoto的扩展熵如何生成一个F次分歧的家庭，导致近似结果，最后以限制方式到Fisher的信息。在目前的论文中，所谓的Tsallis熵用于类似的方式，以产生具有类似特性的新的F分歧。证明了近似性质，其形式明显地概括了上述纸张中的相应结果。

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来源
《South African statistical journal》 |2020年第2期|163-175|共13页
作者
Tertius de Wet; Ferdinand OEsterreicher; Maximilian Thaler;
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作者单位

Department of Statistics and Actuarial Science University of Stellenbosch South Africa;

Department of Mathematics University of Salzburg Austria;

Department of Mathematics University of Salzburg Austria;

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原文格式 PDF
正文语种 eng
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关键词
Dissimilarity measure (f-divergence); Fisher's information; Measure of information (entropy);

机译：不相似度量（F divercence）;费舍尔的信息;信息衡量（熵）;

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1. A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization [J] . SatishKumar, GurdasRam Abstract and applied analysis . 2014,第6期

机译：Havrda-Charvat和Tsallis熵的推广及其公理化
2. A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization [J] . SatishKumar, GurdasRam Abstract and applied analysis . 2014,第2期

机译：Havrda-Charvat和Tsallis熵的推广及其公理化
3. TSALLIS ENTROPY: AXIOMATIC CHARACTERIZATION AND APPLICATION [J] . C. G. CHAKRABARTI, KOYEL GHOSH Modern Physics Letters, B. Condensed Matter Physics, Statistical Physics, Applied Physics . 2009,第23期

机译：TALLIS熵：公理化特征和应用
4. Gibbs-Shannon Entropy and Related Measures: Tsallis Entropy [C] . G. Ramamurthy, T. Jagannadha Swamy International Conference on Communications, Signal Processing, and VLSI . 2019

机译：Gibbs-Shannon熵和相关措施：Tsallis熵
5. A Novel Term Structure Model Based on Tsallis Entropy and Information Geometry. [D] . Yang, Yiping. 2010

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6. A Direct Link between Rényi–Tsallis Entropy and Hölder’s Inequality—Yet Another Proof of Rényi–Tsallis Entropy Maximization [O] . Hisa-Aki Tanaka, Masaki Nakagawa, Yasutada Oohama 2019

机译：Rényi-Tsallis熵与Hölder的不等式 - 尚不公正的Rényi-tsallis熵最大化
7. Tsallis' entropy, modified Newtonian accelerations and the Tully-Fisher relation [O] . Everton M. C. Abreu, Jorge Ananias Neto, Albert C. R. Mendes, 2018

机译：Tsallis'熵，修改牛顿加速度和塔利 - 费舍尔关系
8. Generalized Entropic Uncertainty Relations with Tsallis' Entropy [R] . Portesi, M., Plastino, A. 1996

机译：Tsallis熵的广义熵不确定关系

TSALLIS' ENTROPIES - AXIOMATICS, ASSOCIATED f-DIVERGENCES AND FISHER'S INFORMATION

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