Data depth provides a systematic approach to order multivariate observations in R d . A data depth function is any function D( t; F) that measures the closeness or centrality of a point t ∈ R d with respect to a distribution function F. Thus, a depth function assigns to each x ∈ R d a non-negative score as its center-outward depth with respect to F. Observations close to the center of F receive high ranks whereas peripheral observations receive low ranks.