Compositional Data Modeling through Dirichlet Innovations

Seitebaleng Makgai, Andriette Bekker and Mohammad Arashi
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Seitebaleng Makgai: Department of Statistics, University of Pretoria, Pretoria 0028, South Africa
Andriette Bekker: Department of Statistics, University of Pretoria, Pretoria 0028, South Africa
Mohammad Arashi: Department of Statistics, University of Pretoria, Pretoria 0028, South Africa

Mathematics, 2021, vol. 9, issue 19, 1-18

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.

Keywords: beta function; compositional data; Dirichlet distribution; gamma distribution; Kummer–Dirichlet; outliers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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