We introduce a mixture of generalized hyperbolic distributions as an
alternative to the ubiquitous mixture of Gaussian distributions as well as
their near relatives of which the mixture of multivariate t and skew-t
distributions are predominant. The mathematical development of our mixture of
generalized hyperbolic distributions model relies on its relationship with the
generalized inverse Gaussian distribution. The latter is reviewed before our
mixture models are presented along with details of the aforesaid reliance.
Parameter estimation is outlined within the expectation-maximization framework
before the clustering performance of our mixture models is illustrated via
applications on simulated and real data. In particular, the ability of our
models to recover parameters for data from underlying Gaussian and skew-t
distributions is demonstrated. Finally, the role of Generalized hyperbolic
mixtures within the wider model-based clustering, classification, and density
estimation literature is discussed.