Statistical Modelling 23 (3) (2023), 247–272

Robust clustering based on finite mixture of multivariate fragmental distributions

Mohsen Maleki,
Department of Statistics,
Faculty of Mathematics and Statistics,
University of Isfahan,
Isfahan,
Iran.
e-mail: m.maleki.stat@gmail.com

Geoffrey J McLachlan,
Department of Mathematics,
University of Queensland,
St Lucia,
Australia.

Sharon X Lee,
School of Mathematical Sciences,
University of Adelaide,
Adelaide,
Australia

Abstract:

A flexible class of multivariate distributions called scale mixtures of fragmental normal (SMFN) distributions, is introduced. Its extension to the case of a finite mixture of SMFN (FM-SMFN) distributions is also proposed. The SMFN family of distributions is convenient and effective for modelling data with skewness, discrepant observations, and population heterogeneity. It also posseses some other desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. A stochastic representation of the SMFN distribution is given and then a hierarchical representation is described, the latter aids in parameter estimation, derivation of statistical properties, and simulations. Maximum likelihood estimation of the FM-SMFN distribution via the expectation-maximization (EM) algorithm is outlined before the clustering performance of the proposed mixture model is illustrated using simulated and real datasets. In particular, the ability of FM-SMFN distributions to model data generated from various well-known families is demonstrated.

Keywords:

ECME algorithm; Kurtosis; Maximum likelihood estimates; Multivariate scale mixtures of normal family; Multivariate fragmental distributions

Downloads:

Code in gzipped archive.

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