Asymptotic results for the sum of dependent non-identically distributed random variables

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Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Asymptotic results for the sum of dependent non-identically distributed random variables
Journal
Methodology and Computing in Applied Probability
Author(s)
Kortschak D., Albrecher H.
ISSN
1387-5841
Publication state
Published
Issued date
2009
Peer-reviewed
Oui
Volume
11
Number
3
Pages
279-306
Language
english
Abstract
In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which, even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations for diagonal copulas and t-copulas are given.
Keywords
Subexponential tail, Dependence, Copula, Multivariate regular variation, Maximum domain of attraction
Web of science
Open Access
Yes
Create date
09/02/2009 18:59
Last modification date
20/08/2019 14:53
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