Rates of convergence in certain limit theorem for extreme values
type: Item
instance of: scholarly article
title: Rates of convergence in certain limit theorem for extreme values
zbMATH Open document ID: 1182.62027
author: Pavle Mladenović
author: Jovan Vukmirović
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-12-10T00:00:00Z
review text: Consider an array of random variables \(X_{n1},\dots,X_{nn}\), \(n\in\mathbb{N}\), where in each row \(X_{n1},\dots,X_{nn}\) are independent with common negative binomial distribution with parameters \(r>0\) and \(p=1/n\), \(r\) not necessarily being an integer. It is shown that the limiting distribution of the maximum in each row, suitably standardized, is the Gumbel distribution \(\exp(-e^{-x})\), \(x\in\mathbb{R}\). The rate of pointwise convergence of the distribution functions is established as well. This extends earlier results by the author that were formulated for integer-valued \(r\).
reviewed by: Michael Falk
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62G32
zbMATH DE Number: 5644928
zbMATH Keywords: negative binomial distribution
zbMATH Keywords: gamma function
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.08.044
OpenAlex ID: W1994196277
cites work: Asymptotic Distributions for the Coupon Collector's Problem
cites work: Q3285941
cites work: Q5512461
cites work: Limit theorems for some random variables associated with urn models
cites work: Q4320535
cites work: Limit Theorems for Some Occupancy and Sequential Occupancy Problems
cites work: Some asymptotic results for occupancy problems
cites work: On Birthday, Collectors', Occupancy and Other Classical Urn Problems
cites work: Q5615180
cites work: On some generalized farlie-gumbel-morgenstern distributions-II regression, correlation and further generalizations
cites work: Extremes and related properties of random sequences and processes
cites work: Extremal theory for stochastic processes
cites work: Limit theorems for the maximum terms of a sequence of random variables with marginal geometric distributions
cites work: A Generalization of the Mejzler--de Haan Theorem
cites work: Limit distributions for the problem of collecting pairs
DOI: 10.1016/J.JMAA.2009.08.044
description: scientific article; zbMATH DE number 5644928