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.

翻译：本文提出一种适用于三维角数据（即三维环面上的数据）的新型灵活分布。我们提出的三维包裹柯西连接函数具有以下优势：(i) 密度形式简洁，(ii) 变量对间相关程度可调，(iii) 参数可解释且易于估计，(iv) 条件分布形式已知，(v) 数据生成机制简单，(vi) 单峰性。此外，我们的构建方法允许线性边缘分布，这意味着该连接函数也可用于柱面数据建模。我们阐述了基于最大似然的参数估计方法，并与现有文献中的竞争模型进行了比较，同时分析了两组真实数据：一组涉及蛋白质二面角，另一组来自亚得里亚海浮标观测数据。