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Distortions of multivariate distribution functions and associated level curves: Applications in multivariate risk theory

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  • Di Bernardino, Elena
  • Rullière, Didier

Abstract

In this paper, we propose a parametric model for multivariate distributions. The model is based on distortion functions, i.e. some transformations of a multivariate distribution which permit to generate new families of multivariate distribution functions. We derive some properties of considered distortions. A suitable proximity indicator between level curves is introduced in order to evaluate the quality of candidate distortion parameters. Using this proximity indicator and properties of distorted level curves, we give a specific estimation procedure. The estimation algorithm is mainly relying on straightforward univariate optimizations, and we finally get parametric representations of both multivariate distribution functions and associated level curves. Our results are motivated by applications in multivariate risk theory. The methodology is illustrated on simulated and real examples.

Suggested Citation

  • Di Bernardino, Elena & Rullière, Didier, 2013. "Distortions of multivariate distribution functions and associated level curves: Applications in multivariate risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 190-205.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:190-205
    DOI: 10.1016/j.insmatheco.2013.05.001
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    Cited by:

    1. Elena Di Bernardino & Didier Rullière, 2017. "A note on upper-patched generators for Archimedean copulas," Post-Print hal-01347869, HAL.
    2. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    3. Elena Di Bernardino & Didier Rullière, 2016. "A note on upper-patched generators for Archimedean copulas," Working Papers hal-01347869, HAL.
    4. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1, pages 1-36, October.
    5. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    6. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    7. Coblenz, Maximilian & Grothe, Oliver & Schreyer, Manuela & Trutschnig, Wolfgang, 2018. "On the length of copula level curves," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 347-365.
    8. Elena Di Bernardino & Didier Rullière, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Working Papers hal-01147778, HAL.
    9. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.

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