  A mixture of variance-gamma distributions is introduced and developed for
model-based clustering and classification. The latest in a growing line of
non-Gaussian mixture approaches to clustering and classification, the proposed
mixture of variance-gamma distributions is a special case of the recently
developed mixture of generalized hyperbolic distributions, and a restriction is
required to ensure identifiability. Our mixture of variance-gamma distributions
is perhaps the most useful such special case and, we will contend, may be more
useful than the mixture of generalized hyperbolic distributions in some cases.
In addition to being an alternative to the mixture of generalized hyperbolic
distributions, our mixture of variance-gamma distributions serves as an
alternative to the ubiquitous mixture of Gaussian distributions, which is a
special case, as well as several non-Gaussian approaches, some of which are
special cases. The mathematical development of our mixture of variance-gamma
distributions model relies on its relationship with the generalized inverse
Gaussian distribution; accordingly, the latter is reviewed before our mixture
of variance-gamma distributions is presented. Parameter estimation carried out
within the expectation-maximization framework.
