A new parametric family of distributions on the unit simplex is proposed and investigated. Such family, called flexible Dirichlet, is obtained by normalizing a correlated basis formed by a mixture of independent gamma random variables. The Dirichlet distribution is included as an inner point. The flexible Dirichlet is shown to exhibit a rich dependence pattern, capable of discriminating among many of the independence concepts relevant for compositional data. At the same time it can model multi-modality. A number of stochastic representations are given, disclosing its remarkable tractability. In particular, it is closed under marginalization, conditioning, subcomposition, amalgamation and permutation.

Ongaro, A., Migliorati, S. (2013). A generalization of the Dirichlet distribution. JOURNAL OF MULTIVARIATE ANALYSIS, 114(1), 412-426 [10.1016/j.jmva.2012.07.007].

A generalization of the Dirichlet distribution

ONGARO, ANDREA;MIGLIORATI, SONIA
2013

Abstract

A new parametric family of distributions on the unit simplex is proposed and investigated. Such family, called flexible Dirichlet, is obtained by normalizing a correlated basis formed by a mixture of independent gamma random variables. The Dirichlet distribution is included as an inner point. The flexible Dirichlet is shown to exhibit a rich dependence pattern, capable of discriminating among many of the independence concepts relevant for compositional data. At the same time it can model multi-modality. A number of stochastic representations are given, disclosing its remarkable tractability. In particular, it is closed under marginalization, conditioning, subcomposition, amalgamation and permutation.
Articolo in rivista - Articolo scientifico
Dirichlet mixture; Subcomposition; Amalgamation; Compositional invariance; Neutrality; Multi-modality
English
2013
114
1
412
426
none
Ongaro, A., Migliorati, S. (2013). A generalization of the Dirichlet distribution. JOURNAL OF MULTIVARIATE ANALYSIS, 114(1), 412-426 [10.1016/j.jmva.2012.07.007].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/38015
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