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PolytopeQuantile[{{x11, x12}, ..., {xn1, xn2}}, q]
gives the locus of the q^(th) quantile of the bivariate data, where the data have been ordered using convex hulls centered on ConvexHullMedian[{{x11, x12}, ..., {xn1, xn2}}].
  • Outlying vectors are removed by repeatedly peeling off layers of convex hulls from the data until at most a fraction q are left.
  • PolytopeQuantile interpolates between the convex hulls of the points remaining before and after the last layer is removed.