A note on asymptotics of linear combinations of IID random variables
type: Item
instance of: scholarly article
title: A note on asymptotics of linear combinations of IID random variables
zbMATH Open document ID: 1224.60033
author: Peter Kevei
published in: Periodica Mathematica Hungarica
publication date: 2011-04-26T00:00:00Z
review text: Let \(X_{1},X_{2},\dots\) be i.i.d. random variables with the common distribution function \(F\). For \(n=1,2,\dots\), consider the linear combination \(S_{\boldsymbol{a}_{n}}=a_{n,1}X_{1}+a_{n,2}X_{2}+\cdots +a_{n,n}X_{n}\), where \(\boldsymbol{a}_{n}=\left(a_{n,1} ,a_{n,2}, \dots,a_{n,n}\right)\) is an arbitrary sequence of weights. The author investigates the asymptotic distribution of \(S_{\boldsymbol{a}_{n}}\) under the negligibility condition. He proves that, if \(S_{\boldsymbol{a}_{n}}\) is asymptotically normal, then the distribution \(F\) belongs to the domain of attraction of the 2-stable law.
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 5881206
zbMATH Keywords: linear combinations
zbMATH Keywords: asymptotic normality
zbMATH Keywords: domain of attraction
MaRDI profile type: Publication
full work available at URL: s10998-010-1025-7
OpenAlex ID: W2070503653
Wikidata QID: Q64023164
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DBLP publication ID: journals/pmh/Kevei10
DOI: 10.1007/S10998-010-1025-7
description: scientific article; zbMATH DE number 5881206