  A mixture of shifted asymmetric Laplace distributions is introduced and used
for clustering and classification. A variant of the EM algorithm is developed
for parameter estimation by exploiting the relationship with the general
inverse Gaussian distribution. This approach is mathematically elegant and
relatively computationally straightforward. Our novel mixture modelling
approach is demonstrated on both simulated and real data to illustrate
clustering and classification applications. In these analyses, our mixture of
shifted asymmetric Laplace distributions performs favourably when compared to
the popular Gaussian approach. This work, which marks an important step in the
non-Gaussian model-based clustering and classification direction, concludes
with discussion as well as suggestions for future work.
