ABSTRACT

Mixtures of multiple scaled distributions are a recent addition to the literature on mixture model-based approaches to clustering, classification, and discriminant analysis. After considering mixtures where the component densities parameterize location, scale, concentration, skewness, and index, the next step in increasing modelling flexibility is allowing multiple scaled components. The analysis of the bankruptcy data highlights that the mixture of Coalesced generalized hyperbolic distributions (MCGHD) can give very good clustering performance in scenarios where the Mixture of generalized hyperbolic distributions (MGHD), Mixture of multiple scaled generalized hyperbolic distributions (MMSGHD), and mixture of convex multiple scaled generalized hyperbolic distributions all perform poorly. This is particularly notable in the case of the MGHD and MMSGHD because the MCGHD density arises as a convex combination of their respective densities, cf. Perhaps the most significant point to emerge from the cluster analyses, however, arises from comparison of the MGHD and the MMSGHD results.