A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values
Probability
2013-11-05 v1 Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1311.0540,
title = {A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values},
author = {Ph. Barbe and Miriam Isabel Seifert},
journal= {arXiv preprint arXiv:1311.0540},
year = {2013}
}
Comments
23 pages