Orbital semilinear copulas

Tarad Jwaid; Bernard de Baets; Hans de Meyer

Kybernetika (2009)

  • Volume: 45, Issue: 6, page 1012-1029
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Jwaid, Tarad, Baets, Bernard de, and Meyer, Hans de. "Orbital semilinear copulas." Kybernetika 45.6 (2009): 1012-1029. <http://eudml.org/doc/37691>.

@article{Jwaid2009,
abstract = {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.},
author = {Jwaid, Tarad, Baets, Bernard de, Meyer, Hans de},
journal = {Kybernetika},
keywords = {copula; diagonal section; opposite diagonal section; orbital semilinear copula; semilinear copula; copula; diagonal section; semilinear copula; opposite diagonal section; orbital semilinear copula},
language = {eng},
number = {6},
pages = {1012-1029},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Orbital semilinear copulas},
url = {http://eudml.org/doc/37691},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Jwaid, Tarad
AU - Baets, Bernard de
AU - Meyer, Hans de
TI - Orbital semilinear copulas
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 1012
EP - 1029
AB - 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.
LA - eng
KW - copula; diagonal section; opposite diagonal section; orbital semilinear copula; semilinear copula; copula; diagonal section; semilinear copula; opposite diagonal section; orbital semilinear copula
UR - http://eudml.org/doc/37691
ER -

References

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  12. An Introduction to Copulas, Second edition. Springer, New York, 2006. Zbl1152.62030MR2197664
  13. Diagonal copulas, In: Distributions with given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1977, pp. 121–127. MR1614665
  14. On the construction of copulas and quasi-copula with given diagonal sections, Insurance: Math. Econ. 42 (2008), 473–483. MR2404309
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