A generalization of the Dirichlet distribution

作者：Ongaro A^*; Migliorati S

来源：Journal of Multivariate Analysis, 2013, 114: 412-426.

DOI：10.1016/j.jmva.2012.07.007

• Dirichlet mixture
• Subcomposition
• Amalgamation
• Compositional invariance
• Neutrality
• Multi-modality

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.

• 出版日期2013-2