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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
