Bounds for the difference between median and mean of beta and negative binomial distributions
type: Item
instance of: scholarly article
title: Bounds for the difference between median and mean of beta and negative binomial distributions
zbMATH Open document ID: 0704.60016
DOI: 10.1007/BF02614111
published in: Metrika
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176257
review text: This paper uses the technique developed by \textit{J. Chen} and \textit{H. Rubin} [see Stat. Probab. Lett. 4, 281-283 (1986; Zbl 0596.62015)] to obtain bounds on the difference between the mean and median of the beta distribution and then to solve the same problem for the negative binomial distribution. Theorem 1. Let X have Beta\((p,q)\) distribution. Then \(0<E X-\)median\((X)<A(p,q)=(q-p)/(p+q-2)(p+q)\), \(1<p<q\), \(0<E X-\)median\((X)<A(q,p)\), \(1<q<p,\) and \(E X=\) median\((X)\), \(p=q.\) Theorem 2. Let X have negative bionomial \((r,p)\) distribution. Then \(1<E X-\)median\((X)<(1-p)/p\), \(p<1/2,\) \((1-p)/p<E X-\)median\((X)<1\), \(p>1/2,\) and \(E X=\)median\((X)\), \(p=1/2.\)
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 4155551
zbMATH Keywords: difference between mean and median
zbMATH Keywords: beta distribution
zbMATH Keywords: negative binomial distribution
author: Mark E. Payton
author: Linda J. Young
author: John H. Young
MaRDI profile type: Publication
cites work: Bounds for the difference between median and mean of gamma and Poisson distributions
cites work: THE CRANIAL COORDINATOGRAPH, THE STANDARD PLANES OF THE SKULL, AND THE VALUE OF CARTESIAN GEOMETRY TO THE CRANIOLOGIST, WITH SOME ILLUSTRATIONS OF THE USES OF THE NEW METHOD
OpenAlex ID: W2026295826
description: scientific article; zbMATH DE number 4155551