Distributions on the Simplex Revisited

Gloria Mateu-Figueras (), Gianna S. Monti () and J. J. Egozcue ()
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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

A chapter in Advances in Compositional Data Analysis, 2021, pp 61-82 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-71175-7_4

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DOI: 10.1007/978-3-030-71175-7_4

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