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On the construction of radially symmetric trivariate copulas

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Abstract
We propose a method to construct a 3-dimensional symmetric function that is radially symmetric, using two symmetric 2-copulas, with one of them being also radially symmetric. We study the properties of the presented construction in some specific cases and provide several examples for different families of copulas.
Keywords
Copula, Quasi-copula, Radial symmetry, Aggregation function, AGGREGATION FUNCTIONS, TRANSFORMATIONS, CONCORDANCE

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MLA
Arias García, José De Jesús, et al. “On the Construction of Radially Symmetric Trivariate Copulas.” Soft Methods for Data Science, edited by Maria Brigida Ferraro et al., vol. 456, Springer, 2017, pp. 9–15.
APA
Arias García, J. D. J., De Meyer, H., & De Baets, B. (2017). On the construction of radially symmetric trivariate copulas. In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, M. Á. Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), Soft methods for data science (Vol. 456, pp. 9–15). Cham, Switzerland: Springer.
Chicago author-date
Arias García, José De Jesús, Hans De Meyer, and Bernard De Baets. 2017. “On the Construction of Radially Symmetric Trivariate Copulas.” In Soft Methods for Data Science, edited by Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, María Ángeles Gil, Przemysław Grzegorzewski, and Olgierd Hryniewicz, 456:9–15. Cham, Switzerland: Springer.
Chicago author-date (all authors)
Arias García, José De Jesús, Hans De Meyer, and Bernard De Baets. 2017. “On the Construction of Radially Symmetric Trivariate Copulas.” In Soft Methods for Data Science, ed by. Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, María Ángeles Gil, Przemysław Grzegorzewski, and Olgierd Hryniewicz, 456:9–15. Cham, Switzerland: Springer.
Vancouver
1.
Arias García JDJ, De Meyer H, De Baets B. On the construction of radially symmetric trivariate copulas. In: Ferraro MB, Giordani P, Vantaggi B, Gagolewski M, Gil MÁ, Grzegorzewski P, et al., editors. Soft methods for data science. Cham, Switzerland: Springer; 2017. p. 9–15.
IEEE
[1]
J. D. J. Arias García, H. De Meyer, and B. De Baets, “On the construction of radially symmetric trivariate copulas,” in Soft methods for data science, Rome, Italy, 2017, vol. 456, pp. 9–15.
@inproceedings{8522994,
  abstract     = {{We propose a method to construct a 3-dimensional symmetric function that is radially symmetric, using two symmetric 2-copulas, with one of them being also radially symmetric. We study the properties of the presented construction in some specific cases and provide several examples for different families of copulas.}},
  author       = {{Arias García, José de Jésus and De Meyer, Hans and De Baets, Bernard}},
  booktitle    = {{Soft methods for data science}},
  editor       = {{Ferraro, Maria Brigida and Giordani, Paolo and Vantaggi, Barbara and Gagolewski, Marek and Gil, María Ángeles and Grzegorzewski, Przemysław and Hryniewicz, Olgierd}},
  isbn         = {{9783319429724}},
  issn         = {{2194-5357}},
  keywords     = {{Copula,Quasi-copula,Radial symmetry,Aggregation function,AGGREGATION FUNCTIONS,TRANSFORMATIONS,CONCORDANCE}},
  language     = {{eng}},
  location     = {{Rome, Italy}},
  pages        = {{9--15}},
  publisher    = {{Springer}},
  title        = {{On the construction of radially symmetric trivariate copulas}},
  url          = {{http://dx.doi.org/10.1007/978-3-319-42972-4_2}},
  volume       = {{456}},
  year         = {{2017}},
}

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