Numbers of near-maxima for the bivariate case
type: Item
instance of: scholarly article
title: Numbers of near-maxima for the bivariate case
zbMATH Open document ID: 1247.60071
published in: Statistics \& Probability Letters
publication date: 2010-02-05T00:00:00Z
review text: Let \((X_i,Y_i)\), \(1\leq i\leq n\), be independent and identically distributed random vectors with a continuous distribution function. Put \(X_{n:n}:=\max_{1\leq i\leq n}X_i\) and denote by \(Y_{(n):n}\) the concomitant associated with \(X_{n:n}\). Denote by \(K_n(a,b_1,b_2)\) the number of sample elements that belong to the open rectangle \((X_{n:n}-a,X_{n:n})\times (Y_{(n):n}-b_1,Y_{(n):n}-b_2)\). The authors establish in particular convergence in probability and weak convergence of \(K_n(a,b_1,b_2)\), suitably standardized, as \(n\to\infty\).
reviewed by: Michael Falk
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 5666077
zbMATH Keywords: near-maxima
zbMATH Keywords: bivariate case
zbMATH Keywords: extremes
zbMATH Keywords: concomitants
author: Ismihan Bayramoglu
author: A. Stepanov
MaRDI profile type: Publication
full work available at URL: j.spl.2009.10.007
OpenAlex ID: W1998733232
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DOI: 10.1016/J.SPL.2009.10.007
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description: scientific article; zbMATH DE number 5666077