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