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A generalization of the Dirichlet distribution

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  • Ongaro, A.
  • Migliorati, S.

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.

Suggested Citation

  • Ongaro, A. & Migliorati, S., 2013. "A generalization of the Dirichlet distribution," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 412-426.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:412-426
    DOI: 10.1016/j.jmva.2012.07.007
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    References listed on IDEAS

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    1. Rameshwar D. Gupta & Donald St. P. Richards, 2001. "The History of the Dirichlet and Liouville Distributions," International Statistical Review, International Statistical Institute, vol. 69(3), pages 433-446, December.
    2. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    3. Ng, Kai Wang & Tang, Man-Lai & Tan, Ming & Tian, Guo-Liang, 2008. "Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 490-509, March.
    4. Gupta, Rameshwar D. & Richards, Donald St.P., 1987. "Multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 233-256, December.
    5. Gupta, Rameshwar D. & Richards, Donald St. P., 1992. "Multivariate Liouville distributions, III," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 29-57, October.
    6. Gupta, R. D. & Richards, D. S. P., 1995. "Multivariate Liouville Distributions, IV," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 1-17, July.
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