The family of circular distributions based on non-negative trigonometric sums (NNTS), developed by Fernández-Durán (2004), is highly flexible for modeling datasets exhibiting multimodality and/or skewness. In this article, we extend the NNTS family to axial data by identifying conditions under which the original NNTS family is suitable for modeling undirected vectors. Since the estimation is performed using maximum likelihood, likelihood ratio tests are developed for characteristics of the density function such as uniformity and symmetry, as well as to compare different axial populations through homogeneity tests. The proposed methodology is applied to real datasets involving orientations of rocks, animals, and plants.

翻译：由Fernández-Durán（2004）提出的基于非负三角和（NNTS）的圆形分布族，对于呈现多模态和/或偏态的数据集建模具有高度灵活性。本文通过识别原始NNTS族适用于无方向向量建模的条件，将该分布族扩展至轴向数据。由于采用最大似然法进行估计，我们开发了似然比检验，用于检验密度函数的特性（如均匀性和对称性），并通过同质性检验比较不同的轴向总体。所提出的方法已应用于涉及岩石、动物和植物方向的实际数据集。