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Shannon entropy: axiomatic characterization and application [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon ...
C. G. Chakrabarti, Indranil Chakrabarty
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Adaptive estimation of Shannon entropy [PDF]
2015 IEEE International Symposium on Information Theory (ISIT), 2015 We consider estimating the Shannon entropy of a discrete distribution $P$ from $n$ i.i.d. samples. Recently, Jiao, Venkat, Han, and Weissman, and Wu and Yang constructed approximation theoretic estimators that achieve the minimax $L_2$ rates in estimating entropy.
Han, Yanjun +2 more
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On the Characterization of Shannon’s Entropy by Shannon’s Inequality [PDF]
Journal of the Australian Mathematical Society, 1973 1. In [2,5,6,7] a.o. several interpretations of the inequalityfor allsuch thatwere given and the following was proved.
Aczél, J., Ostrowski, A. M.
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Shannon Entropy Estimation for Linear Processes [PDF]
Journal of Risk and Financial Management, 2020 In this paper, we estimate the Shannon entropy S(f)=−E[log(f(x))] of a one-sided linear process with probability density function f(x). We employ the integral estimator Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely and in Ł2 under reasonable conditions.
Timothy Fortune, Hailin Sang
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Application of Positional Entropy to Fast Shannon Entropy Estimation for Samples of Digital Signals
Entropy, 2020 This paper introduces a new method of estimating Shannon entropy. The proposed method can be successfully used for large data samples and enables fast computations to rank the data samples according to their Shannon entropy.
Marcin Cholewa, Bartłomiej Płaczek
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Shannon Entropy Reinterpreted [PDF]
Reports on Mathematical Physics, 2018 In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k \sum_{i} W^{-1} \circ \mathsf{ln}(p_{i})$.
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Tsallis Wavelet Entropy and Its Application in Power Signal Analysis
Entropy, 2014 As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory.
Jikai Chen, Guoqing Li
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Maximal Shannon entropy in the vicinity of an exceptional point in an open microcavity
Scientific Reports, 2020 The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy is maximized near the EP in the parameter space for two interacting
Kyu-Won Park +3 more
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Extended Shannon entropies. II [PDF]
Czechoslovak Mathematical Journal, 1983 This paper examines functionals (called extended Shannon entropies), defined for all probability spaces equipped with a measurable metric, and coinciding with Shannon entropy for finite probability spaces endowed with the metric \(d(x,y)=1\), \(x\neq y\).
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Research on the Source Convergence Diagnose Method of Monte Carlo Critical Calculation for Loosely Coupled System [PDF]
EPJ Web of ConferencesIn order to improve the reliability and accuracy of Monte Carlo program in the critical safety calculation of loosely coupled systems, an improved Shannon entropy diagnose method considering the distribution of fission sources and the statistical bias is
Cheng Yuting +5 more
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