Extremal limit laws for discrete random variables
type: Item
instance of: scholarly article
title: Extremal limit laws for discrete random variables
zbMATH Open document ID: 1072.60013
DOI: 10.1023/B:JOTH.0000031884.79099.71
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-28T00:00:00Z
review text: Let \(X\) be a discrete random variable taking the nonnegative integers with probability mass function Pr\((X=k)=p_k\). Let \(X_1, X_2, \dots, X_n\) be independent and identically distributed copies of \(X\) and let us denote the maximum by \(m_n=\max(x_1,\dots,x_n)\). Consider the limiting distribution of \(M_n=(m_n-b(n))/a(n)\), as \(n\to \infty\), for some real numbers \(a(n)\) and \(b(n)\). It is known for distributions such as the Poisson and geometric distributions, that the limiting distribution is not nondegenerate. However, if Poisson random variable with parameter \(\lambda(n)\) is alloved to vary with respect to \(n\) in a suitable manner, the limiting distribution of \(M_n\) can be nondegenerate. The aim of this paper is to show how the above development could be emulated for other well-known discrete distributions including the uniform, binomial, geometric, negative binomial ones.
reviewed by: N. G. Gamkrelidze
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 2183288
zbMATH Keywords: Poisson, geometric, binomial, negative binomial distribution
author: Saralees Nadarajah
author: K. V. Mitov
MaRDI profile type: Publication
full work available at URL: b:joth.0000031884.79099.71
OpenAlex ID: W2085749932
description: scientific article; zbMATH DE number 2183288