Univariate conditioning of copulas

Radko Mesiar; Vladimír Jágr; Monika Juráňová; Magda Komorníková

Kybernetika (2008)

  • Volume: 44, Issue: 6, page 807-816
  • ISSN: 0023-5954

Abstract

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The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter λ > 0 allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter μ ∈ [0,λ].

How to cite

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Mesiar, Radko, et al. "Univariate conditioning of copulas." Kybernetika 44.6 (2008): 807-816. <http://eudml.org/doc/33966>.

@article{Mesiar2008,
abstract = {The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter λ > 0 allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter μ $\in $ [0,λ].},
author = {Mesiar, Radko, Jágr, Vladimír, Juráňová, Monika, Komorníková, Magda},
journal = {Kybernetika},
keywords = {conditioning; gluing; g-ordinal sum; construction of copulas; conditioning; gluing; -ordinal sum; construction of copulas},
language = {eng},
number = {6},
pages = {807-816},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Univariate conditioning of copulas},
url = {http://eudml.org/doc/33966},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Mesiar, Radko
AU - Jágr, Vladimír
AU - Juráňová, Monika
AU - Komorníková, Magda
TI - Univariate conditioning of copulas
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 6
SP - 807
EP - 816
AB - The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter λ > 0 allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter μ $\in $ [0,λ].
LA - eng
KW - conditioning; gluing; g-ordinal sum; construction of copulas; conditioning; gluing; -ordinal sum; construction of copulas
UR - http://eudml.org/doc/33966
ER -

References

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  10. Klement E. P., Mesiar, R., Pap E., Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms, Fuzzy Sets and Systems 104 (1999), 3–14 (1999) Zbl0953.26008MR1685803
  11. Mesiar R., Szolgay J., W -ordinal sums of copulas and quasi-copulas, In: Proc. MAGIA 2004 Conference, Kočovce 2004, pp. 78–83 
  12. Nelsen R. B., An Introduction to Copulas, Second edition. Springer, Berlin 2006 Zbl1152.62030MR2197664
  13. Siburg K. F., Stoimenov P. A., 10.1080/03610920802074844, Comm. Statist. A – Theory Methods 37 (2008), 3124–3134 MR2467756DOI10.1080/03610920802074844
  14. Sklar M., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 (1959) MR0125600

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