Department

Mathematics

Document Type

Article

Publication Date

2-26-2019

Abstract

In the present paper, we prove that the probabilities of the Pólya urn distribution (with negative replacement) satisfy a monotonicity property similar to that of the binomial distribution. As a consequence, we show that the corresponding random variables are stochastically ordered with respect to the parameter giving the initial distribution of the urn. An equivalent formulation of this result shows that the new Bernstein–Stancu-type operator introduced in (Pascu et al. in Proc. Rom. Acad., Ser. A: Math. Phys. Tech. Sci. Inf. Sci. 2019, in press) is a monotone operator. The proofs are probabilistic in spirit and rely on various inequalities, some of which are of independent interest (e.g., a refined version of the reversed Cauchy–Bunyakovsky–Schwarz inequality or estimates of the error of approximating an integral by the trapezoidal rule).

Journal

Journal of Inequalities and Applications

Journal ISSN

1025-5834

Volume

47

Digital Object Identifier (DOI)

10.1186/s13660-019-2004-z

Comments

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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