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.
