A generalization of Lévy's concentration-variance inequality
type: Item
instance of: scholarly article
title: A generalization of Lévy's concentration-variance inequality
zbMATH Open document ID: 0682.60013
DOI: 10.1007/BF01207513
author: Yanyan Li
publication date: 1990-01-01T00:00:00Z
review text: Sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function \(\phi\). In the case \(\phi (x)=(x-c)^ 2\), where c is the expected value of the distribution, these bounds yield the classical concentration-variance inequality of Lévy. An analogous sharp inequality is obtained in a similar linear search setting, where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length.
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 4117544
zbMATH Keywords: Levy concentration function
zbMATH Keywords: linear search problem
zbMATH Keywords: concentration- variance inequality
MaRDI profile type: Publication
cites work: On the linear search problem
cites work: Q5560061
cites work: Q4079613
cites work: Linear search with bounded resources
cites work: Q4086490
full work available at URL: https://doi.org/10.1007/bf01207513
OpenAlex ID: W2042113397
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4117544