Complete monotonicity of some entropies

被引：0
作者：
Ioan Raşa
机构：
[1] Technical University of Cluj-Napoca,Department of Mathematics
来源：
Periodica Mathematica Hungarica | 2017年 / 75卷
关键词：
Entropies; Concavity; Complete monotonicity; Inequalities; 94A17; 60E15; 26A51;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and negative binomial distributions) and investigate their Shannon, Rényi, and Tsallis entropies with respect to complete monotonicity.
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页码：159 / 166
页数：7
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共 15 条
  • [1] Abel U(2015)Complete monotonicity and zeros of sums of squared Baskakov functions Appl. Math. Comput. 258 130-137
  • [2] Gawronski W(2010)Sharp bounds on the entropy of the Poisson Law and related quantities IEEE Trans. Inf. Theory 56 2299-2306
  • [3] Neuschel Th(2007)Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions J. Approx. Theory 149 131-150
  • [4] Adell JA(2014)On a conjecture concerning the sum of the squared Bernstein polynomials Appl. Math. Comput. 241 70-74
  • [5] Lekuona A(2001)Binomial and Poisson distributions as maximum entropy distributions IEEE Trans. Inf. Theory 47 2039-2041
  • [6] Yu Y(2012)Concavity of entropy along binomial convolutions Electron. Commun. Prob. 17 1-9
  • [7] Berdysheva E(1998)Integral representations and asymptotic expansions for Shannon and Rényi entropies Appl. Math. Lett. 11 69-74
  • [8] Gavrea I(2014)Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa J. Math. Anal. Appl. 418 852-860
  • [9] Ivan M(2015)Entropies and Heun functions associated with positive linear operators Appl. Math. Comput. 268 422-431
  • [10] Harremoës P(1988)Possible generalization of Boltzmann–Gibbs statistics J. Stat. Phys. 52 479-487
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