Multimodal Distributions for Circular Axial Data

Abstract

The family of circular distributions based on non-negative trigonometric sums (NNTS), developed by Fern\'andez-Dur\'an (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.