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

Juan Fernández Sánchez and Wolfgang Trutschnig

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 5, 1508-1526

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.

Date: 2016
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DOI: 10.1080/03610926.2013.864856

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