Pair Copula Decompositions and Constructions

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.