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.

Mateu-Figueras, G., Monti, G., Egozcue, J. (2021). Distributions on the simplex revisited. In P. Filzmoser, K. Hron, J.A. Martin-Fernandez, J. Palarea-Albaladejo (a cura di), Advances in Compositional Data Analysis Festschrift in Honour of Vera Pawlowsky-Glahn (pp. 61-82). Springer International Publishing [10.1007/978-3-030-71175-7_4].

Distributions on the simplex revisited

Monti, GS;
2021

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.
Capitolo o saggio
shifted-scaled Dirichlet distribution; Aitchison geometry; Normal in the Simplex
English
Advances in Compositional Data Analysis Festschrift in Honour of Vera Pawlowsky-Glahn
Filzmoser, P; Hron, K; Martin-Fernandez, JA; Palarea-Albaladejo, J
2021
978-3-030-71174-0
Springer International Publishing
61
82
Mateu-Figueras, G., Monti, G., Egozcue, J. (2021). Distributions on the simplex revisited. In P. Filzmoser, K. Hron, J.A. Martin-Fernandez, J. Palarea-Albaladejo (a cura di), Advances in Compositional Data Analysis Festschrift in Honour of Vera Pawlowsky-Glahn (pp. 61-82). Springer International Publishing [10.1007/978-3-030-71175-7_4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/316306
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