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arXiv · 1811.03827

Convex order for convolution polynomials of Borel measures

Andrzej Komisarski·Teresa Rajba
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Abstract

We give necessary and sufficient conditions for Borel measures to satisfy the inequality introduced by Komisarski, Rajba (2018). This inequality is a generalization of the convex order inequality for binomial distributions, which was proved by Mrowiec, Rajba, Wąsowicz (2017), as a probabilistic version of the inequality for convex functions, that was conjectured as an old open problem by I.~Raşa. We present also further generalizations using convex order inequalities between convolution polynomials of finite Borel measures. We generalize recent results obtained by B.~Gavrea (2018) in the discrete case to general case. We give solutions to his open problems and also formulate new problems.

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Andrzej Komisarski, Teresa Rajba. 2018-11-09. Convex order for convolution polynomials of Borel measures. https://arxiv.org/abs/1811.03827

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