A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values

We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to infinity. As a consequence, we derive conditional limit t...

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Bibliographic Details
Published in:arXiv.org 2013-11
Main Authors: Barbe, Ph, Seifert, Miriam Isabel
Format: Article
Language:English
Subjects:
Bivariate analysis
Extreme values
Mathematical analysis
Random variables
Real variables
Theorems
Online Access:Get full text
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Summary:We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to infinity. As a consequence, we derive conditional limit theorems for random pairs (X,Y)=(Ru(T),Rv(T)) given that X is large. These results imply earlier ones which were obtained in the literature under stronger assumptions.
ISSN:2331-8422