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Compositional Data Modeling through Dirichlet Innovations

Author

Listed:
  • Seitebaleng Makgai

    (Department of Statistics, University of Pretoria, Pretoria 0028, South Africa
    These authors contributed equally to this work.)

  • Andriette Bekker

    (Department of Statistics, University of Pretoria, Pretoria 0028, South Africa
    These authors contributed equally to this work.)

  • Mohammad Arashi

    (Department of Statistics, University of Pretoria, Pretoria 0028, South Africa
    Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran)

Abstract

The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, in the presence of outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary. In this paper, the Kummer–Dirichlet distribution and the gamma distribution are coupled, using the beta-generating technique. This development results in the proposal of the Kummer–Dirichlet gamma distribution, which presents greater flexibility in modeling compositional data sets. Some general properties, such as the probability density functions and the moments are presented for this new candidate. The method of maximum likelihood is applied in the estimation of the parameters. The usefulness of this model is demonstrated through the application of synthetic and real data sets, where outliers are present.

Suggested Citation

  • Seitebaleng Makgai & Andriette Bekker & Mohammad Arashi, 2021. "Compositional Data Modeling through Dirichlet Innovations," Mathematics, MDPI, vol. 9(19), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2477-:d:649532
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    References listed on IDEAS

    as
    1. Thomas, Seemon & Jacob, Joy, 2006. "A generalized Dirichlet model," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1761-1767, October.
    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.
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