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Distributions on the Simplex Revisited

In: Advances in Compositional Data Analysis

Author

Listed:
  • Gloria Mateu-Figueras

    (University of Girona, Department of Computer Science, Applied Mathematics and Statistics)

  • Gianna S. Monti

    (University of Milan-Bicocca, Department of Economics, Management and Statistics)

  • J. J. Egozcue

    (Technical University of Catalonia, Department of Applied Mathematics III)

Abstract

A large number of families of distributions are available to model multivariate real vectors. On the contrary, for the simplex sample space, we have only a limited number of families arising through the generalization of the Dirichlet family or the logratio normal family. This chapter tries to summarize those models and some generalizations with a special emphasis on the algebraic-geometric structure of the simplex and on the measure which is considered compatible. In particular, the shifted-scaled Dirichlet distribution is studied and the logratio t distribution is rewritten and studied with respect to the Aitchison measure.

Suggested Citation

  • Gloria Mateu-Figueras & Gianna S. Monti & J. J. Egozcue, 2021. "Distributions on the Simplex Revisited," Springer Books, in: Peter Filzmoser & Karel Hron & Josep Antoni Martín-Fernández & Javier Palarea-Albaladejo (ed.), Advances in Compositional Data Analysis, pages 61-82, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-71175-7_4
    DOI: 10.1007/978-3-030-71175-7_4
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