  Zonoid depth, as a well-known ordering tool, has been widely used in
multivariate analysis. However, since its depth value vanishes outside the
convex hull of the data cloud, it suffers from the so-called `outside problem',
which consequently hinders its many practical applications, e.g.,
classification. In this note, we propose a new class of \emph{$L_q$-norm zonoid
depths}, which has no such problem. Examples are also provided to illustrate
their contours.
