ABSTRACT
The multivariate normal distribution remains a central choice for modelling continuous multivariate data. An alternative to add flexibility is to use parametric distributions with skewness and thick tails that robustify inference while keeping interpretation and computations manageable. The generalization introduces d new parameters directly interpretable in terms of the B. Arnold–R. A. Groeneveld measure of skewness, and allows adapting existing computational strategies. An interesting feature of two-piece distributions is leading to easily interpretable parameters. A likelihood- or posterior-based fitted mixture inherently aims to approximate the underlying data-generating pdf rather than the number of clusters; for example, a single non-normal cluster may be captured by introducing several normal components. Model-based clustering can often be adjusted to account for deviations from normality in a manner that is conceptually straightforward and retains both computational tractability and ease of interpretation.
