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Some members of the class of (quasi-)copulas with given diagonal from the Markov kernel perspective

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  • Juan Fernández Sánchez
  • Wolfgang Trutschnig

Abstract

Calculating Markov kernels of copulas allows not only for a precise description of the way Bertino- and diagonal copulas distribute mass, but also enables a simply proof of the fact that, for certain diagonals, both may degenerate to proper generalized shuffles of the minimum copula. After extending the kernel approach to the case of the maximum quasi-copula Aδ with given diagonal δ, a conjecture on singularity of Aδ by Nelsen et al. (2008) is established and an alternative simple and short proof of the result by Úbeda-Flores (2008) characterizing diagonals for which Aδ is a copula is given.

Suggested Citation

  • Juan Fernández Sánchez & Wolfgang Trutschnig, 2016. "Some members of the class of (quasi-)copulas with given diagonal from the Markov kernel perspective," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1508-1526, March.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:5:p:1508-1526
    DOI: 10.1080/03610926.2013.864856
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    Citations

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    Cited by:

    1. Kasper Thimo M. & Fuchs Sebastian & Trutschnig Wolfgang, 2021. "On convergence of associative copulas and related results," Dependence Modeling, De Gruyter, vol. 9(1), pages 307-326, January.
    2. Fabrizio Durante & Juan Fernández Sánchez & Wolfgang Trutschnig, 2020. "Spatially homogeneous copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 607-626, April.
    3. Kamnitui Noppadon & Trutschnig Wolfgang & Fernández-Sánchez Juan, 2018. "Maximum asymmetry of copulas revisited," Dependence Modeling, De Gruyter, vol. 6(1), pages 47-62, February.
    4. Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.

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