Baker's Distribution, Bernstein Copula and B-spline Copula

Abstract

We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions as well as the dependence structure of bivariate order statistics. Since the copula of Baker's distribution can be considered as the Bernstein copula in terms of a finite mixture distribution, we propose EM algorithms to estimate the Bernstein copula. We also propose the B-spline copula and show that the B-spline copula includes the Bernstein copula as a special case. The B-spline copula inherits nice properties from the Bernstein copula and has more flexibility in representing correlations. With minor changes, the EM algorithm designed for the Bernstein copula is applicable for the B-spline copula. (This is a joint work with S. Kuriki, G. D. Lin and D. Richards.)