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Bivariate Copulas Based on Counter-Monotonic Shock Method

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.)

  • Nicola Sottocornola

    (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’Informatiques, Université du Québec à Trois-Rivières, Trois- Rivières, QC G8Z 4M3, Canada
    These authors contributed equally to this work.)

Abstract

This paper explores the properties of a family of bivariate copulas based on a new approach using the counter-monotonic shock method. The resulting copula covers the full range of negative dependence induced by one parameter. Expressions for the copula and density are derived and many theoretical properties are examined thoroughly, including explicit expressions for prominent measures of dependence, namely Spearman’s rho, Kendall’s tau and Blomqvist’s beta. The convexity properties of this copula are presented, together with explicit expressions of the mixed moments. Estimation of the dependence parameter using the method of moments is considered, then a simulation study is carried out to evaluate the performance of the suggested estimator. Finally, an application of the proposed copula is illustrated by means of a real data set on air quality in New York City.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:11:p:202-:d:951495
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    References listed on IDEAS

    as
    1. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, vol. 50(2), pages 383-391, March.
    2. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    3. Genest, Christian & Mesfioui, Mhamed & Schulz, Juliana, 2018. "A new bivariate Poisson common shock model covering all possible degrees of dependence," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 202-209.
    4. Ruiz-Rivas, Carmen & Cuadras, Carles M., 1988. "Inference properties of a one-parameter curved exponential family of distributions with given marginals," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 447-456, November.
    5. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
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