Bernshtein's interpolational polynomials
type: Item
instance of: scholarly article
title: Bernshtein's interpolational polynomials
zbMATH Open document ID: 0879.41007
author: V. I. Zubov
published in: Doklady Mathematics
publication date: 1997-12-17T00:00:00Z
review text: This paper states without proof six theorems about approximation of distributions of random variables by interpolatory polynomials. The main result is Theorem 1: Let \(F_0\) be a strictly monotonic continuous probability distribution. Then for each \(n\) and each monotonic sequence \(0\leq b_1 \leq b_2 \leq \dots \leq b_n=1\) the function \[ \sum_{j=1}^n b_j {n \choose j }(1-F_0(x))^{n-j}F_0(x)^j \tag{1} \] is a continuous probability distribution. Each continuous probability distribution \(F(x)\) can be approximated in the uniform norm by linear combinations (1) with suitable numbers \(n\) and \(b_j\).
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1050594
zbMATH Keywords: uniform approximation
zbMATH Keywords: distribution functions
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1050594