Weak convergence and the Prokhorov radius
type: Item
instance of: scholarly article
title: Weak convergence and the Prokhorov radius
zbMATH Open document ID: 0755.60017
DOI: 10.1016/0022-247X(92)90266-G
author: George A. Anastassiou
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The Prokhorov radius \(D(a,b,t,s)\) is defined as the supremum of the Prokhorov (Ky Fan) distance \[ d(X,a)=\inf\{r>0,\;\text{Pr}(| X- a|>r)<r\} \] over the set \(M(a,b,t,s)\) of real-valued random variables \(X\) with mean \(m\) and variance \(V\) satisfying the inequality constraints \(| m-a|<t\) and \(| V-b|<s\). Using the Kemperman geometric approach to certain moment problems, the author computes the value of \(D(a,b,t,s)\).
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 62787
zbMATH Keywords: Prokhorov metric
zbMATH Keywords: geometric approach
zbMATH Keywords: moment problems
reviewed by: Svetlozar T. Rachev
MaRDI profile type: Publication
cites work: The Lévy radius of a set of probability measures satisfying basic moment conditions involving \(\{t,t^ 2\}\)
cites work: The General Moment Problem, A Geometric Approach
cites work: Q3203758
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description: scientific article; zbMATH DE number 62787