<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

Published Online: Feb 01, 2023

Page range: 111 - 126

Received: Nov 05, 2022

Accepted: Jan 20, 2023

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

Keywords
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

Published Online: Feb 01, 2023

Page range: 111 - 126

Received: Nov 05, 2022

Accepted: Jan 20, 2023

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

KeywordsBivariate 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.

Keywords
Bivariate copula, FGM copulas, Asymmetry, Concordance and perturbation