Geodesic
Orbital semilinear copulas
Kybernetika, Tome 45 (2009) no. 6, pp. 1012-1029.

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We introduce four families of semilinear copulas (i.e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital semilinear copulas, which are obtained by linear interpolation on segments connecting the diagonal and opposite diagonal of the unit square.
Classification : 62H05, 62H10, 62H20
Keywords: copula; diagonal section; opposite diagonal section; orbital semilinear copula; semilinear copula 
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     title = {Orbital semilinear copulas},
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Jwaid, Tarad; Baets, Bernard de; Meyer, Hans de. Orbital semilinear copulas. Kybernetika, Tome 45 (2009) no. 6, pp. 1012-1029. http://geodesic.mathdoc.fr/item/KYB_2009__45_6_a9/