Sharp inequalities between skewness and kurtosis for unimodal distributions
type: Item
instance of: scholarly article
title: Sharp inequalities between skewness and kurtosis for unimodal distributions
zbMATH Open document ID: 0820.60009
DOI: 10.1016/0167-7152(94)00074-I
published in: Statistics \& Probability Letters
publication date: 1995-04-02T00:00:00Z
review text: Let \(X\) be a random variable with zero mean and unit variance and define \(\gamma_ 1 = E(X^ 3)\), \(\gamma_ 2 = E(X^ 4) - 3\). The main result is an upper bound for \(\gamma_ 2\) in terms of \(\gamma_ 1\) in the case that \(X\) has a unimodal distribution with support \([a,b]\), where \(a + b \geq 0\). The bound is sharp.
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 739587
zbMATH Keywords: inequalities
zbMATH Keywords: skewness
zbMATH Keywords: kurtosis
zbMATH Keywords: unimodal distribution
author: Friedrich Teuscher
author: Volker Guiard
reviewed by: M. P. Quine
MaRDI profile type: Publication
cites work: Q5624436
cites work: The Moment Problem for Unimodal Distributions
cites work: Q3238726
cites work: Sharp inequalities between skewness and kurtosis
cites work: Table of the bounds of the probability integral when the first four moments are given
cites work: A Note on Skewness and Kurtosis
full work available at URL: 0167-7152(94)00074-i
OpenAlex ID: W1983540233
description: scientific article; zbMATH DE number 739587