  This article proposes a new class of Real Elliptically Skewed (RESK)
distributions and associated clustering algorithms that allow for integrating
robustness and skewness into a single unified cluster analysis framework.
Non-symmetrically distributed and heavy-tailed data clusters have been reported
in a variety of real-world applications. Robustness is essential because a few
outlying observations can severely obscure the cluster structure. The RESK
distributions are a generalization of the Real Elliptically Symmetric (RES)
distributions. To estimate the cluster parameters and memberships, we derive an
expectation maximization (EM) algorithm for arbitrary RESK distributions.
Special attention is given to a new robust skew-Huber M-estimator, which is
also the maximum likelihood estimator (MLE) for the skew-Huber distribution
that belongs to the RESK class. Numerical experiments on simulated and
real-world data confirm the usefulness of the proposed methods for skewed and
heavy-tailed data sets.
