<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>New copulas, based on perturbation theory, are introduced to clarify a <italic>symmetrization</italic> procedure for asymmetric copulas. We give also some properties of the <italic>symmetrized</italic> copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.</p>
</abstract>

New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the...

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Publié en ligne: 01 févr. 2023

Pages: 111 - 126

Reçu: 05 nov. 2022

Accepté: 20 janv. 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0008

Mots clés
Bivariate copula, FGM copulas, Asymmetry, Concordance and perturbation

© 2023 Mohamed El maazouz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Publié en ligne: 01 févr. 2023

Pages: 111 - 126

Reçu: 05 nov. 2022

Accepté: 20 janv. 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0008

Mots clésBivariate copula, FGM copulas, Asymmetry, Concordance and perturbation

© 2023 Mohamed El maazouz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Bivariate copula, FGM copulas, Asymmetry, Concordance and perturbation