The logratio Student’s t distribution: a robust model for compositional data analysis

Abstract We introduce and study the logratio Student’s t distribution as a robust and flexible alternative to the classical logratio normal model for compositional data. This distribution preserves the geometric coherence of the Aitchison simplex framework while accommodating heavier tails, enabling improved detection of outliers — an essential feature in many real-world applications. Our main contribution is to formally embed the t distribution within the logratio framework and to demonstrate its equivalence across logratio representations for the purposes of estimation and outlier detection, while clarifying the distinct mathematical properties of each representation beyond distribution fitting. Monte Carlo simulations under scale contamination show that our model, combined with a Leave-One-Out procedure, outperforms traditional robust methods (MCD, COMCoDa) by ensuring higher AUC and near-perfect specificity, even in high dimensions. A real-world application illustrates the model’s superior ability to uncover structure and identify outliers in multivariate compositional data. These results position the logratio t distribution as a theoretically sound and practically powerful tool for robust inference in the simplex.