  The assumption of normality in data has been considered in the field of
statistical analysis for a long time. However, in many practical situations,
this assumption is clearly unrealistic. It has recently been suggested that the
use of distributions indexed by skewness/shape parameters produce more
exibility in the modelling of different applications. Consequently, the results
show a more realistic interpretation for these problems. For these reasons, the
aim of this paper is to investigate the effects of the generalisation of a
discrimination function method through the class of multivariate extended
skew-elliptical distributions, study in detail the multivariate extended
skew-normal case and develop a quadratic approximation function for this family
of distributions. A simulation study is reported to evaluate the adequacy of
the proposed classification rule as well as the performance of the EM algorithm
to estimate the model parameters.
