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The family of location and scale mixtures of Gaussians has the ability togenerate a number of flexible distributional forms. It nests as particularcases several important asymmetric distributions like the GeneralisedHyperbolic distribution. The Generalised Hyperbolic distribution in turn nestsmany other well known distributions such as the Normal Inverse Gaussian (NIG)whose practical relevance has been widely documented in the literature. In amultivariate setting, we propose to extend the standard location and scalemixture concept into a so called multiple scaled framework which has theadvantage of allowing different tail and skewness behaviours in each dimensionof the variable space with arbitrary correlation between dimensions. Estimationof the parameters is provided via an EM algorithm with a particular focus onNIG distributions. Inference is then extended to cover the case of mixtures ofsuch multiple scaled distributions for application to clustering. Assessmentson simulated and real data confirm the gain in degrees of freedom andflexibility in modelling data of varying tail behaviour and directional shape.

Clustering using skewed multivariate heavy tailed distributions with flexible tail behaviour