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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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Citation

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Chicago
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. Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, María Ángeles Gil, Przemysław Grzegorzewski, and Olgierd Hryniewicz, 456:9–15. Cham, Switzerland: Springer.
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). Presented at the 8th International conference on Soft Methods in Probability and Statistics (SMPS-2016), 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.
MLA
Arias García, José De Jesús, Hans De Meyer, and Bernard De Baets. “On the Construction of Radially Symmetric Trivariate Copulas.” Soft Methods for Data Science. Ed. Maria Brigida Ferraro et al. 456. Cham, Switzerland: Springer, 2017. 9–15. Print.
@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 Garc{\'i}a, Jos{\'e} De Jes{\'u}s 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, Mar{\'i}a {\'A}ngeles and Grzegorzewski, Przemys\unmatched{0142}aw and Hryniewicz, Olgierd},
  isbn         = {9783319429724},
  issn         = {2194-5357},
  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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