A note on equal distributions
type: Item
instance of: scholarly article
title: A note on equal distributions
zbMATH Open document ID: 0584.62017
DOI: 10.1007/BF02481983
author: Gwo Dong Lin
published in: Annals of the Institute of Statistical Mathematics
publication date: 1984-01-01T00:00:00Z
review text: For each \(n\geq 1\), let \(X_{1,n}\leq X_{2,n}\leq...\leq X_{n,n}\) denote the ordered observations based on a random sample of size n from an arbitrary probability distribution F with finite mean. \textit{W. Hoeffding} [Ann. Math. Stat. 24, 93-100 (1953; Zbl 0050.136)] showed that the sequence \(\{E(X_{k,n}):1\leq k\leq n\), \(n\geq 1\}\) determines F. More recently, \textit{M. Pollak} [Ann. Stat. 1, 180-182 (1973; Zbl 0263.62008)] has given an improved version of Hoeffding's result. In the present note, Hoeffding's result is improved further.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 30B60
zbMATH DE Number: 3936176
zbMATH Keywords: equal distributions
zbMATH Keywords: identifiability
zbMATH Keywords: characterizations
zbMATH Keywords: completeness
zbMATH Keywords: order statistics
reviewed by: Damodar Shanbhag
MaRDI profile type: Publication
cites work: Characterization of distributions by sets of moments of order statistics
cites work: On the Distribution of the Expected Values of the Order Statistics
cites work: A note on Bernstein and Müntz-Szasz theorems with applications to the order statistics
cites work: On equal distributions
full work available at URL: https://doi.org/10.1007/bf02481983
OpenAlex ID: W1980789750
description: scientific article; zbMATH DE number 3936176