Geodesic
Univariate conditioning of copulas
Kybernetika, Tome 44 (2008) no. 6, pp. 807-816 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\in $ [0,λ].
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].
Classification : 60E05, 62H05
Keywords: conditioning; gluing; g-ordinal sum; construction of copulas 
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     author = {Mesiar, Radko and J\'agr, Vladim{\'\i}r and Jur\'a\v{n}ov\'a , Monika and Komorn{\'\i}kov\'a, Magda},
     title = {Univariate conditioning of copulas},
     journal = {Kybernetika},
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Mesiar, Radko; Jágr, Vladimír; Juráňová , Monika; Komorníková, Magda. Univariate conditioning of copulas. Kybernetika, Tome 44 (2008) no. 6, pp. 807-816. http://geodesic.mathdoc.fr/item/KYB_2008_44_6_a5/

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