A generalization of the Dirichlet distribution

A. Ongaro and S. Migliorati

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 412-426

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.

Keywords: Dirichlet mixture; Subcomposition; Amalgamation; Compositional invariance; Neutrality; Multi-modality (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:114:y:2013:i:c:p:412-426

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DOI: 10.1016/j.jmva.2012.07.007

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