Characterizations of Archimedean n -copulas

Włodzimierz Wysocki

Kybernetika (2015)

  • Volume: 51, Issue: 2, page 212-230
  • ISSN: 0023-5954

Abstract

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We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.

How to cite

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Wysocki, Włodzimierz. "Characterizations of Archimedean $n$-copulas." Kybernetika 51.2 (2015): 212-230. <http://eudml.org/doc/270090>.

@article{Wysocki2015,
abstract = {We present three characterizations of $n$-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an $n$-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.},
author = {Wysocki, Włodzimierz},
journal = {Kybernetika},
keywords = {Archimedean operation; additive generator; diagonal generator; multiplicative generator; (Archimedean) $n$-copula; (Archimedean) $n$-quasicopula; Archimedean operation; additive generator; diagonal generator; multiplicative generator; (Archimedean) $n$-copula; (Archimedean) $n$-quasicopula},
language = {eng},
number = {2},
pages = {212-230},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Characterizations of Archimedean $n$-copulas},
url = {http://eudml.org/doc/270090},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Wysocki, Włodzimierz
TI - Characterizations of Archimedean $n$-copulas
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 2
SP - 212
EP - 230
AB - We present three characterizations of $n$-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an $n$-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.
LA - eng
KW - Archimedean operation; additive generator; diagonal generator; multiplicative generator; (Archimedean) $n$-copula; (Archimedean) $n$-quasicopula; Archimedean operation; additive generator; diagonal generator; multiplicative generator; (Archimedean) $n$-copula; (Archimedean) $n$-quasicopula
UR - http://eudml.org/doc/270090
ER -

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