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Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

1
Department of Statistics, College of Sciences, Shiraz University, Shiraz 71946 85115, Iran
2
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
3
Department of Statistics, Faculty of Science, Fasa University, Fasa 74616 86131, Iran
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 38; https://doi.org/10.3390/axioms8020038
Received: 18 February 2019 / Revised: 15 March 2019 / Accepted: 27 March 2019 / Published: 1 April 2019
In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models. View Full-Text
Keywords: ECME algorithm; finite mixture model; maximum likelihood estimates; scale mixtures of normal family; two-piece distributions ECME algorithm; finite mixture model; maximum likelihood estimates; scale mixtures of normal family; two-piece distributions
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Maleki, M.; Contreras-Reyes, J.E.; Mahmoudi, M.R. Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family. Axioms 2019, 8, 38.

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