New bounds for the extreme values of a finite sample of real numbers
type: Item
instance of: scholarly article
title: New bounds for the extreme values of a finite sample of real numbers
zbMATH Open document ID: 0869.49017
author: Alberto Seeger
author: J.-P. Crouzeix
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-21T00:00:00Z
review text: This paper deals with the problem of estimating the smallest value \(x_{\min}\) and the largest value \(x_{\max}\) of a finite collection of unknown real numbers. The only information available on this collection is its average and its standard deviation. The authors derive new bounds by solving two optimization problems, one of them being convex and the other nonconvex. They show that the pair \((x_{\min}, x _{\max})\) lies in a region bounded by an ellipse and a hyperbola whose Cartesian equations are given in terms of the average and standard deviation of the collection.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C90
zbMATH DE Number: 902449
zbMATH Keywords: convex
zbMATH Keywords: nonconvex
zbMATH Keywords: optimization problem
reviewed by: M. Zuhair Nashed
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0029
OpenAlex ID: W1986127620
DOI: 10.1006/JMAA.1996.0029
description: scientific article; zbMATH DE number 902449