In this paper, we propose a new flexible family of distributions for data that consist of three angles, two angles and one linear component, or one angle and two linear components. To achieve this, we equip the recently proposed trivariate wrapped Cauchy copula with non-uniform marginals and develop a parameter estimation procedure. We compare our model to its main competitors for analyzing trivariate data and provide some evidence of its advantages. We illustrate our new model using toroidal data from protein bioinformatics of conformational angles, and cylindrical data from climate science related to buoy in the Adriatic Sea. The paper is motivated by these real trivariate datasets.

翻译：本文提出了一种适用于由三个角度、两个角度与一个线性分量、或一个角度与两个线性分量组成的数据的新型灵活分布族。为实现此目标，我们将最近提出的三变量环绕柯西连接函数与非均匀边缘分布相结合，并开发了参数估计方法。我们将该模型与处理三变量数据的主要竞争模型进行比较，并提供了其优势的证据。我们通过蛋白质生物信息学中构象角的环形数据，以及气候科学中与亚得里亚海浮标相关的柱面数据，展示了新模型的应用。本文的动机源于这些真实的三变量数据集。