Multivariate Bernstein Frechet copulas

Finding joint copulas based on given bivariate margins is an interesting problem. It involves in obtaining the copula from the information of its bivariate marginal distributions. In this paper, we present a multivariate copula family called multivariate Bernstein Frechet (BF) copulas. Each copula in the family is uniquely determined by its bivariate margins, the bivariate BF copulas. For this purpose, we first discuss properties of the bivariate BF copulas, including super-migrativity and TP2 properties. The advantages of bivariate BF copula are identified by comparing it with the bivariate Gaussian copula and the bivariate Frechet copula. We show that a multivariate BF copula is uniquely determined by its marginal bivariate BF copulas, and methods to construct the multivariate BF copula are discussed. Numerical studies are carried out for displaying the advantages of multivariate BF copulas.