<div class="csl-bib-body">
<div class="csl-entry">Heiny, J. (2013). <i>Multivariate extremes and dependence structures : a theoretical background for modelling</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2013.20672</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2013.20672
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/4178
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dc.description.abstract
Many fields of modern science have to deal with events which are rare but of outstanding importance. Extreme value theory is a practical and useful mathematical tool for modelling events which occur with very small probability. In a wide variety of applications these extreme events have an inherently multivariate character. This thesis provides an overview of the relevant theoretical results for modelling multivariate extremes and their dependence structures. We study multivariate extreme value distributions (MEVDs) and characterise their maximum domain of attraction (MDA). We state the relationships between four equivalent representations of MEVDs which can be used as a basis for estimation. Moreover we look at tail dependence coefficients and provide information about the underlying dependence. The central result is the multivariate extension of the Fisher-Tippett Theorem which basically says that the maximum domain of attraction of a MEVD is characterised by the univariate MDAs of its margins and a so-called copula domain of attraction (CDA) of its copula. We construct explicit examples of copulas which are in no CDA and describe models for the tail of a multivariate distribution function. In order to facilitate model building, some methods to construct new extreme value copulas from known ones are presented.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.title
Multivariate extremes and dependence structures : a theoretical background for modelling
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2013.20672
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Johannes Heiny
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC11164577
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dc.description.numberOfPages
60
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-73731
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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tuw.advisor.orcid
0000-0001-9588-8249
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item.languageiso639-1
en
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item.fulltext
with Fulltext
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item.openaccessfulltext
Open Access
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item.mimetype
application/pdf
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item.openairetype
master thesis
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item.grantfulltext
open
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.cerifentitytype
Publications
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crisitem.author.dept
E105 - Institut für Stochastik und Wirtschaftsmathematik