Invariance of relative inverse function orderings under compositions of distributions
type: Item
instance of: scholarly article
title: Invariance of relative inverse function orderings under compositions of distributions
zbMATH Open document ID: 1261.60026
author: Magdalena Frąszczak
author: Jarosław Bartoszewicz
published in: Applicationes Mathematicae
publication date: 2012-09-26T00:00:00Z
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 6086606
zbMATH Keywords: convex order
zbMATH Keywords: dispersive order
zbMATH Keywords: star order
zbMATH Keywords: superadditive order
zbMATH Keywords: orbits
zbMATH Keywords: general order statistics
zbMATH Keywords: maximal invariant
zbMATH Keywords: distance between distribution functions
MaRDI profile type: Publication
full work available at URL: am39-3-3
OpenAlex ID: W2334991941
DOI: 10.4064/AM39-3-3
review text: Let \(\mathcal{F}\) denote the class of continuous distributions on \([0,\infty)\) and let \(\mathbf{\Psi}\) be the class of continuous strictly increasing distribution functions on \([0,1]\). Let \(\leq_S\) be a preorder in \(\mathcal{F}\). The preorder \(\leq_S\) is said to be invariant under the class \(\mathbf{\Psi}\) if \(F\leq_S G\Rightarrow\psi F\leq_S\psi G\) for all \(\psi\in\mathbf{\Psi}\). The authors show that the function \(\lambda(t)=G^{-1}F(t)\), \(t>0\), is a maximal invariant under the group \(\mathbf{\Psi}\). As a result, the convex, star, superadditive, dispersive, and usual stochastic orders are invariant under that group. Some results about ordering the orbits and distances between ordered distributions are also given.
reviewed by: Moshe Shaked
description: scientific article; zbMATH DE number 6086606