Estimates for the stability of decompositions of three-point distributions
type: Item
instance of: scholarly article
title: Estimates for the stability of decompositions of three-point distributions
zbMATH Open document ID: 0928.62015
DOI: 10.1007/BF02465578
published in: Lithuanian Mathematical Journal
publication date: 1999-06-14T00:00:00Z
review text: Let \(\rho(F,G)= \sup_x| F(x)- G(x)|\) denote the uniform (Kolmogorov) distance of two distribution functions \(F\) and \(G\). The main result of this paper seems to be following: For any sequence of convolutions \(F_n= F_{n1}* F_{n2}\) and any discontinuous distribution function \(G\) satisfying \(\rho (F_n,G)\to 0\) as \(n\to \infty\) the relation \[ \inf_{G_{n1} *G_{n2}=G} \max_{j=1, 2} \rho(F_{nj},G_{nj}) \to 0\quad\text{as }n\to \infty \] holds.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1296184
zbMATH Keywords: decomposition of distributions
zbMATH Keywords: stability
zbMATH Keywords: Kolmogorov metric
author: J. J. Mačys
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
cites work: Stability of decomposition into components of a discontinuous distribution function in uniform metric
cites work: Modern Theory of Summation of Random Variables
full work available at URL: https://doi.org/10.1007/bf02465578
OpenAlex ID: W2091012303
description: scientific article; zbMATH DE number 1296184