Abstract
The goal is to construct multivariate distributions using only bivariate building blocks. The appropriate tool to obtain such a construction is to use conditioning. (Rüschendorf, Schweizer and Taylor (Ed.), Distributions with Fixed Marginals and Related Topics, 1996) Joe (1996) gave the first pair copula construction of a multivariate copula in terms of distribution functions, while (Proceedings of ESREL2001. Turin, Italy, 2001) Bedford and Cooke (2001), (Annals of Statistics, 30(4):1031–1068, 2002) Bedford and Cooke (2002) independently developed constructions expressed in terms of densities. Additionally they provided a general framework to identify all possible constructions.
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Czado, C. (2019). Pair Copula Decompositions and Constructions. In: Analyzing Dependent Data with Vine Copulas. Lecture Notes in Statistics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-030-13785-4_4
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DOI: https://doi.org/10.1007/978-3-030-13785-4_4
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