  The simplicial depth, like other relevant multivariate statistical data depth
functions, vanishes right outside the convex hull of the support of the
distribution with respect to which the depth is computed. This is problematic
when it is required to differentiate among points outside the convex hull of
the distribution support, with respect to which the depth is computed, based on
their depth values. We provide the first proposal for simplicial depth which do
not vanish right outside the convex hull of the distribution. The properties of
the proposal and of the corresponding estimator are studied theoretically and
by means of Monte Carlo simulations and analysis of datasets.
