  We give a quantitative interpretation of the Frequent Hypercyclicity
Criterion. Actually we show that an operator which satisfies the Frequent
Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A
refers to some weighted densities sharper than the natural lower density. In
that order, we exhibit different scales of weighted densities that are of
interest to quantify the "frequency" measured by the Frequent Hypercyclicity
Criterion. Moreover we construct an example of unilateral weighted shift which
is frequently hypercyclic but not A-frequently hypercyclic on a particular
scale.
