Trivariate Burr-III copula with applications to income data

Abstract

In this work, Bivariate Burr-III copula is extended to the trivariate case. This copula seems to be very general and analytically manageable and it provides an alternative to the commonly employed elliptical copulas (such as the Gaussian or the Stutent’s t ones) since they have, roughly, the same number of parameters. Several applications to income and wine data are described in the paper. They show that the Trivariate Burr-III copula is, in general, able to capture the dependence structure implicit in observed trivariate data. Moreover, they show that the third-order interaction parameter results, in some cases, significant at $1\%$ significance level while, in other cases, it can be removed from the fitted model. The ability of the Trivariate Burr-III copula in representing the dependence structure implicit in the considered data is compared with the ones of other well known copulas: the Clayton copula, the t copula, and the Skew-t copula. It results that the Trivariate Burr-III copula provides a good fitting and turns out to be the best performer in fitting the considered wine data but, on income data, the best performers are the t and Skew-t copulas. The over-performance of the last two copulas on income data is probably due to their ability in representing right-tail dependence (a kind of dependence that is not taken into account by the Trivariate Burr-III copula).