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Asymptotics of joint maxima for discontinuous random variables


Feidt, A; Genest, C; Nešlehová, J (2010). Asymptotics of joint maxima for discontinuous random variables. Extremes, 13(1):35-53.

Abstract

This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous case, the latter is characterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on recent work of Coles and Pauli (Stat Probab Lett 54:373-379, 2001) and Mitov and Nadarajah (Extremes 8:357-370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data Anal 16:279-297, 1993) in the discontinuous case.

Abstract

This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous case, the latter is characterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on recent work of Coles and Pauli (Stat Probab Lett 54:373-379, 2001) and Mitov and Nadarajah (Extremes 8:357-370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data Anal 16:279-297, 1993) in the discontinuous case.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:March 2010
Deposited On:11 Nov 2010 12:11
Last Modified:07 Dec 2017 03:23
Publisher:Springer
ISSN:1386-1999
Publisher DOI:https://doi.org/10.1007/s10687-009-0085-7

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