  We give a finitary criterion for the convergence of measures on
non-elementary geometrically finite hyperbolic orbifolds to the unique measure
of maximal entropy. We give an entropy criterion controlling escape of mass to
the cusps of the orbifold. Using this criterion we prove new results on the
distribution of collections of closed geodesics on such orbifold, and as a
corollary we prove equidistribution of closed geodesics up to a certain length
in amenable regular covers of geometrically finite orbifolds.
