Characterizations of distributions via two expected values of order statistics
type: Item
instance of: scholarly article
title: Characterizations of distributions via two expected values of order statistics
zbMATH Open document ID: 0654.62021
DOI: 10.1007/BF02613321
author: Jun Shung Hwang
author: Gwo Dong Lin
published in: Metrika
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176199
review text: Let \(X_{k,n}\) be the k-th smallest order statistic of a random sample of size n from a distribution F(x) with \(E| X| <\infty\). Then in general two expected values of order statistics, say E \(X_{k,n}\) and E \(X_{\ell,m}\), are not enough to characterize F in the class of all distributions on the real line \(R\equiv (-\infty,\infty)\). However, in the following class of distributions associated with any fixed non- degenerate distribution \(F_ 0\) through the location and scale parameters, \[ {\mathcal F}_{F_ 0}=\{F_{\mu,\sigma}:\quad F_{\mu,\sigma}(x)=F_ 0((x-\mu)/\sigma)\quad on\quad R,\quad \mu \in R,\quad \sigma >0\}, \] F is characterized by any pair E \(X_{k,n}\) and E \(X_{\ell,m}\) with indices satisfying the condition: \[ (\ell -k, m- n)\not\in \{(a,b):\quad a=b=0\quad or\quad 0<a<b\quad or\quad b<a<0\}. \] Three special cases concerning the uniform, exponential and logistic distributions are investigated completely.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4068062
zbMATH Keywords: characterization
zbMATH Keywords: expected values of order statistics
zbMATH Keywords: location
zbMATH Keywords: scale
zbMATH Keywords: logistic distributions
MaRDI profile type: Publication
cites work: Some properties of partial sums of the harmonic series
cites work: On the Distribution of the Expected Values of the Order Statistics
cites work: Q3334783
cites work: Q3788875
OpenAlex ID: W2017891671
description: scientific article; zbMATH DE number 4068062