Inferential methods for the spherical-Dirichlet distribution

This paper advances the theoretical foundation of the spherical-Dirichlet distribution (SDD) by developing a comprehensive inferential framework, including a closed-form Fisher information matrix and likelihood ratio tests for key directional hypotheses. In contrast to earlier studies that emphasized the generative and geometric aspects of the SDD, we focus on constructing concrete tools for statistical inference, such as tests for uniformity and for the equality of directional means within this constrained manifold setting. The resulting Fisher information facilitates both efficient computation and asymptotic analysis of maximum likelihood estimators. Through simulation studies, we validate chi-square approximations and demonstrate robust performance in finite samples. Finally, an established case study from the wine chemistry literature underscores the practical relevance of the proposed methods.