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Robust clustering from incomplete data is an important topic because, in manypractical situations, real data sets are heavy-tailed, asymmetric, and/or havearbitrary patterns of missing observations. Flexible methods and algorithms formodel-based clustering are presented via mixture of the generalized hyperbolicdistributions and its limiting case, the mixture of multivariate skew-tdistributions. An analytically feasible EM algorithm is formulated forparameter estimation and imputation of missing values for mixture modelsemploying missing at random mechanisms. The proposed methodologies areinvestigated through a simulation study with varying proportions of syntheticmissing values and illustrated using a real dataset. Comparisons are made withthose obtained from the traditional mixture of generalized hyperbolicdistribution counterparts by filling in the missing data using the meanimputation method.

Mixtures of Generalized Hyperbolic Distributions and Mixtures of Skew-t Distributions for Model-Based Clustering with Incomplete Data