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Diverse copulas through Durante’s method. Exploring parametric functions

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  • Christophe Chesneau

Abstract

This article unveils the often underestimated potential of a copula methodology introduced by Durante in 2009. It highlights the remarkable ability of the method to generate a broad spectrum of copulas by exploiting various parametric functions. Our exploration encompasses a collection of power-like, exponential-like, trigonometric-like, logarithmic-like, hyperbolic-like and error-like functions, each dependent on one, two, or three parameters, effectively satisfying the necessary assumptions of Durante’s method. The proofs provided rely on suitable differentiation, comprehensive factorizations, and judicious application of mathematical inequalities. In the vast repertoire of copulas derived from this methodology, we present three distinct series of eight new copulas, supported by a graphical analysis of their respective densities. This theoretical study not only expands the understanding of copula generation but also introduces a new perspective on their construction in various contexts.

Suggested Citation

  • Christophe Chesneau, 2024. "Diverse copulas through Durante’s method. Exploring parametric functions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 61-86.
    • Handle: RePEc:wut:journl:v:34:y:2024:i:3:p:61-86:id:4
    DOI: 10.37190/ord240304
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    References listed on IDEAS

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    1. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, vol. 50(2), pages 383-391, March.
    2. Farid El Ktaibi & Rachid Bentoumi & Nicola Sottocornola & Mhamed Mesfioui, 2022. "Bivariate Copulas Based on Counter-Monotonic Shock Method," Risks, MDPI, vol. 10(11), pages 1-20, October.
    3. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    4. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
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