Summary
In this paper we study the problem of the compatibility of three bivariate copulas, i.e., we look for conditions which allow us to assure the existence of a three-copula whose two-dimensional margins are given. As a particular case, we seek conditions for two bivariate copulasC 1 andC 2 under whichC 2[C1 (x, y), z] is a three-copula. We specifically study the compatibility of the copulasM, W andII with other copulas both in general and in the particular case. We also study the compatibility of a two-copula with convex linear combinations of other two-copulas. Several examples illustrate the results obtained in each case, and some applications are given.
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Quesada-Molina, J.J., Rodríguez-Lallena, J.A. Some advances in the study of the compatibility of three bivariate copulas. J. It. Statist. Soc. 3, 397–417 (1994). https://doi.org/10.1007/BF02589026
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DOI: https://doi.org/10.1007/BF02589026