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On the Ratio-Type Family of Copulas

Author

Listed:
  • Farid El Ktaibi

    (Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates
    These authors contributed equally to this work.)

  • Rachid Bentoumi

    (Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates
    These authors contributed equally to this work.)

  • Mhamed Mesfioui

    (Département de Mathématiques et d’Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada
    These authors contributed equally to this work.)

Abstract

Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form u v / ( 1 − θ f ( u ) g ( v ) ) . It includes numerous examples and discusses the admissible range of parameter θ , showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, u v / ( 1 − θ ϕ ( u , v ) ) , and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ -inversion, and the moment copula method.

Suggested Citation

  • Farid El Ktaibi & Rachid Bentoumi & Mhamed Mesfioui, 2024. "On the Ratio-Type Family of Copulas," Mathematics, MDPI, vol. 12(11), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1743-:d:1407983
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    References listed on IDEAS

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    3. Patricia Mariela Morillas, 2005. "A method to obtain new copulas from a given one," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 169-184, April.
    4. S. Izadkhah & H. Ahmadzade & M. Amini, 2015. "Further Results for a General Family of Bivariate Copulas," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3146-3157, August.
    5. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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