an:06126050
Zbl 1258.60020
Ongaro, A.; Migliorati, S.
A generalization of the Dirichlet distribution
EN
J. Multivariate Anal. 114, 412-426 (2013).
00312699
2013
j
60E05 62E15 62H05
Dirichlet mixture; subcomposition; amalgamation; compositional invariance; neutrality; multi-modality
Summary: 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.