  In this paper, we will present a new flexible distribution for
three-dimensional angular data, or data on the three-dimensional torus. Our
trivariate wrapped Cauchy copula has the following benefits: (i) simple form of
density, (ii) adjustable degree of dependence between every pair of variables,
(iii) interpretable and well-estimable parameters, (iv) well-known conditional
distributions, (v) a simple data generating mechanism, (vi) unimodality.
Moreover, our construction allows for linear marginals, implying that our
copula can also model cylindrical data. Parameter estimation via maximum
likelihood is explained, a comparison with the competitors in the existing
literature is given, and two real datasets are considered, one concerning
protein dihedral angles and another about data obtained by a buoy in the
Adriatic Sea.
