Convex Ordering of Pólya Random Variables and Approximation Monotonicity of Bernstein–Stancu Operators
Department
Mathematics
Document Type
Article
Publication Date
2-1-2023
Abstract
In the present paper we show that in Pólya’s urn model, for an arbitrarily fixed initial distribution of the urn, the corresponding random variables satisfy a natural convex ordering with respect to the replacement parameter. As an application, we show that in the class of convex functions, the error of approximation for Bernstein–Stancu operators is a non-decreasing (strictly increasing under an additional hypothesis) function of the corresponding parameter. The proofs rely on two results of independent interest: an interlacing lemma of three sets and the monotonicity of the (partial) first moment of Pólya random variables with respect to the replacement parameter.
Journal Title
Results in Mathematics
Journal ISSN
14226383
Volume
78
Issue
1
Digital Object Identifier (DOI)
10.1007/s00025-022-01802-5