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Semiquadratic copulas based on horizontal and vertical interpolation

Tarad Jwaid (UGent) , Bernard De Baets (UGent) and Hans De Meyer (UGent)
(2015) FUZZY SETS AND SYSTEMS. 264. p.3-21
Author
Organization
Abstract
We introduce several families of semiquadratic copulas (i.e. copulas that are quadratic in any point of the unit square in at least one coordinate) of which the diagonal and/or opposite diagonal sections are given functions. These copulas are constructed by quadratic interpolation on segments connecting the diagonal, opposite diagonal and sides of the unit square; all interpolations are therefore performed horizontally or vertically. For each family we provide the necessary and sufficient conditions on the given diagonal and/or opposite diagonal functions and two auxiliary real functions to obtain a copula that has these diagonal and/or opposite diagonal functions as diagonal and/or opposite diagonal sections. Just as the product copula is a central member of all families of semilinear copulas based on horizontal and vertical interpolation, it turns out that the Farlie Gumbel Morgenstern family of copulas is included in all families of semiquadratic copulas introduced and characterized here.
Keywords
Quasi-copula, Quadratic interpolation, Copula, OPPOSITE DIAGONAL SECTIONS, SEMILINEAR COPULAS, AGGREGATION FUNCTIONS, QUASI-COPULAS, CONSTRUCTION

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MLA
Jwaid, Tarad, et al. “Semiquadratic Copulas Based on Horizontal and Vertical Interpolation.” FUZZY SETS AND SYSTEMS, vol. 264, 2015, pp. 3–21, doi:10.1016/j.fss.2014.04.023.
APA
Jwaid, T., De Baets, B., & De Meyer, H. (2015). Semiquadratic copulas based on horizontal and vertical interpolation. FUZZY SETS AND SYSTEMS, 264, 3–21. https://doi.org/10.1016/j.fss.2014.04.023
Chicago author-date
Jwaid, Tarad, Bernard De Baets, and Hans De Meyer. 2015. “Semiquadratic Copulas Based on Horizontal and Vertical Interpolation.” FUZZY SETS AND SYSTEMS 264: 3–21. https://doi.org/10.1016/j.fss.2014.04.023.
Chicago author-date (all authors)
Jwaid, Tarad, Bernard De Baets, and Hans De Meyer. 2015. “Semiquadratic Copulas Based on Horizontal and Vertical Interpolation.” FUZZY SETS AND SYSTEMS 264: 3–21. doi:10.1016/j.fss.2014.04.023.
Vancouver
1.
Jwaid T, De Baets B, De Meyer H. Semiquadratic copulas based on horizontal and vertical interpolation. FUZZY SETS AND SYSTEMS. 2015;264:3–21.
IEEE
[1]
T. Jwaid, B. De Baets, and H. De Meyer, “Semiquadratic copulas based on horizontal and vertical interpolation,” FUZZY SETS AND SYSTEMS, vol. 264, pp. 3–21, 2015.
@article{5946192,
  abstract     = {{We introduce several families of semiquadratic copulas (i.e. copulas that are quadratic in any point of the unit square in at least one coordinate) of which the diagonal and/or opposite diagonal sections are given functions. These copulas are constructed by quadratic interpolation on segments connecting the diagonal, opposite diagonal and sides of the unit square; all interpolations are therefore performed horizontally or vertically. For each family we provide the necessary and sufficient conditions on the given diagonal and/or opposite diagonal functions and two auxiliary real functions to obtain a copula that has these diagonal and/or opposite diagonal functions as diagonal and/or opposite diagonal sections. Just as the product copula is a central member of all families of semilinear copulas based on horizontal and vertical interpolation, it turns out that the Farlie Gumbel Morgenstern family of copulas is included in all families of semiquadratic copulas introduced and characterized here.}},
  author       = {{Jwaid, Tarad and De Baets, Bernard and De Meyer, Hans}},
  issn         = {{0165-0114}},
  journal      = {{FUZZY SETS AND SYSTEMS}},
  keywords     = {{Quasi-copula,Quadratic interpolation,Copula,OPPOSITE DIAGONAL SECTIONS,SEMILINEAR COPULAS,AGGREGATION FUNCTIONS,QUASI-COPULAS,CONSTRUCTION}},
  language     = {{eng}},
  pages        = {{3--21}},
  title        = {{Semiquadratic copulas based on horizontal and vertical interpolation}},
  url          = {{http://doi.org/10.1016/j.fss.2014.04.023}},
  volume       = {{264}},
  year         = {{2015}},
}
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