Limit theorems of general functions of independent and identically distributed random variables
type: Item
instance of: scholarly article
title: Limit theorems of general functions of independent and identically distributed random variables
zbMATH Open document ID: 1185.60022
author: K. Nidhin
author: C. Chandran
published in: Statistics \& Probability Letters
publication date: 2009-11-18T00:00:00Z
review text: Let \(\{X_n, n\geq 1\}\) be a sequence of independent and identically random variables and \(g(X_1,\dots,X_N)\) a measurable function of \(X_1,\dots, X_N)\), where \(N= n\) or \(N\) is a positive integer-valued random variable independent of \((X_n)\). It is proved that if \(g\) fulfils a certain divisibility condition and under proper normalization \(g(X_1,\dots,X_N)\) converges in distribution to a limiting random variable \(Z\), then \(Z\) is degenerate or satisfies some stability property defined by \(g\). Limit distributions for sums, maxima and minima, both for random and non-random \(N\), are presented as applications of the main theorem.
reviewed by: T. Inglot
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 5634852
zbMATH Keywords: functions of independent and identically distributed random variables
zbMATH Keywords: limiting distribution
zbMATH Keywords: central limit theorem
zbMATH Keywords: extreme value theorem
zbMATH Keywords: random sample size
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.spl.2009.08.013
OpenAlex ID: W2000477605
cites work: Q5560061
cites work: Sample extremes: an elementary introduction
cites work: Q5541610
cites work: Q4526186
cites work: Extremes and related properties of random sequences and processes
cites work: Q4653585
cites work: Maximum stability and a generalization
cites work: Characterization of the logistic and loglogistic distributions by extreme value related stability with random sample size
DOI: 10.1016/J.SPL.2009.08.013
description: scientific article; zbMATH DE number 5634852