Almost sure limit points of sample extremes of an i.i.d. sequence
type: Item
instance of: scholarly article
title: Almost sure limit points of sample extremes of an i.i.d. sequence
zbMATH Open document ID: 0639.60035
DOI: 10.1007/BF01903614
author: S. S. Nayak
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: Let \((X_ n\), \(n\geq 1)\) be a sequence of independent and identically distributed random variables with a common distribution function F which has a positive derivative for large x and for such x let \[ g(x)=((1- F(x))/f(x))\log \log (1/(1-F(x))). \] We obtain the almost sure limit sets of the random vector consisting of the first two largest values (properly normalized) in a random sample on F in the following two cases: 1) \(\lim_{x\to \infty}g(x)/x=c\) \((0\leq c<\infty),\) 2) F(x) is twice differentiable with \(\lim_{x\to \infty}g'(x)=0\).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 4042950
zbMATH Keywords: limit point
zbMATH Keywords: sample extremes
zbMATH Keywords: almost sure limit sets
MaRDI profile type: Publication
cites work: The Rate of Growth of Sample Maxima
cites work: Q4162318
cites work: On the sequence of partial maxima of some random sequences
cites work: Almost sure limit points of independent copies of sample maxima
cites work: A functional law of the iterated logarithm for maximum of Gaussian sequences
cites work: A law of the iterated logarithm for extreme values from gaussian sequences
cites work: Almost sure limit points of maxima of stationary Gaussian sequences
cites work: On the functional form of the law of the iterated logarithm for the partial maxima of independent identically distributed random variables
description: scientific article; zbMATH DE number 4042950