  Skew-elliptical distributions constitute a large class of multivariate
distributions that account for both skewness and a variety of tail properties.
This class has simpler representations in terms of densities rather than
cumulative distribution functions, and the tail density approach has previously
been developed to study tail properties when multivariate densities have more
tractable forms. The special skew-elliptical structure allows for derivations
of specific forms for the tail densities for those skew-elliptical copulas that
admit probability density functions, under heavy and light tail conditions on
density generators. The tail densities of skew-elliptical copulas are explicit
and depend only on tail properties of the underlying density generator and
conditions on the skewness parameters. In the heavy tail case skewness
parameters affect tail densities of the skew-elliptical copulas more profoundly
than that in the light tail case, whereas in the latter case the tail densities
of skew-elliptical copulas are only proportional to the tail densities of
symmetrical elliptical copulas. Various examples, including tail densities of
skew-normal and skew-t distributions, are given.
