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Convexity properties of some entropies. (English) Zbl 1448.94118

Summary: We consider a family of probability distributions depending on a real parameter \(x\), and study the logarithmic convexity of the sum of the squared probabilities. Applications concerning bounds and concavity properties of Rényi and Tsallis entropies are given. Finally, some extensions and an open problem are presented.
For Part II, see [Result. Math. 74, No. 4, Paper No. 154, 9 p. (2019; Zbl 1429.26016)].

MSC:

94A17 Measures of information, entropy
26A51 Convexity of real functions in one variable, generalizations
26D05 Inequalities for trigonometric functions and polynomials
60E05 Probability distributions: general theory

Citations:

Zbl 1429.26016
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References:

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