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Threshold copulas and positive dependence

Author

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  • Durante, Fabrizio
  • Foschi, Rachele
  • Spizzichino, Fabio

Abstract

Starting with a notion of positive dependence and with the family of the lower threshold copulas Ct associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas Ct for some t. Then, we analyze some structural aspects of lower threshold copulas and of the given definitions. Furthermore we consider several specific cases arising from relevant special choices of (e.g., PQD, LTD, TP2 and PLR). Our analysis, in particular, allows us to present a number of relevant examples and counter-examples, which can be useful in the study of the tail dependence for a bivariate distribution.

Suggested Citation

  • Durante, Fabrizio & Foschi, Rachele & Spizzichino, Fabio, 2008. "Threshold copulas and positive dependence," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2902-2909, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2902-2909
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    References listed on IDEAS

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    1. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    2. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
    3. George Kimeldorf & Allan Sampson, 1989. "A framework for positive dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 31-45, March.
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    Cited by:

    1. Hashorva, Enkelejd & Jaworski, Piotr, 2012. "Gaussian approximation of conditional elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 397-407.
    2. Zorgati, Imen & Lakhal, Faten & Zaabi, Elmoez, 2019. "Financial contagion in the subprime crisis context: A copula approach," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 269-282.
    3. Zalzadeh, Saeed & Pellerey, Franco, 2016. "A positive dependence notion based on componentwise unimodality of copulas," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 51-57.
    4. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    5. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS

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