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This is a continuation of the author’s paper “Convexity properties of some entropies”, published in Raşa (Results Math 73:105, 2018). We consider the sum $$F_n(x)$$ Fn(x) of the squared fundamental Bernstein polynomials of degree n, in relation with Rényi entropy and Tsallis entropy for the binomial distribution with parameters n and x. Several functional equations and inequalities for these functions...
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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