Modeling Random Compositions: The Logratio t-Student Distribution

G. Mateu-Figueras, G. S. Monti, V. Pawlowsky-Glahn, J. J. Egozcue

In the analysis of random compositions, we have a limited number of families of distributions to model random vectors constrained to the simplex. The two most commonly used families are the Dirichlet distribution and its generalizations, derived from perturbation and power transformation on the simplex, and the logratio-normal family, also known as the normal on the simplex or the logistic normal distribution.
In this presentation, we introduce a new family of distributions on the unit simplex using the multivariate t-Student model, which we refer to as the logratio t-Student distribution. We explore its representation through the algebraic-geometric structure of the simplex and examine its main properties while considering the Aitchison measure. Furthermore, we establish its connection with the previously introduced additive logistic t model. Finally, we present an application using a real data set and we analyse its relationship with the atypicality index for detecting outliers.

Palabras clave: Multivariate t-Student distribution compositional data orthonormal basis

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