  Using a Monte Carlo method, we have directly extracted from the available
measurements, the hierarchies among the different elements of the quark mass
matrices. To do that, we have first introduced a model independent
parameterization for two generic class of models: those based on Abelian
symmetries and those inspired by a U(2) horizontal symmetry. So, matrix entries
are proportional to some epsilon^t, with epsilon<<1 and the t's are different
free exponents that we determine from the data through a statistically well
defined procedure. We have found that the experimental data poorly constrain
the Abelian scenarios. Instead, in non Abelian scenarios, these t-exponents are
strongly constrained by the present data. We have found that contrary to a
naive U(2) horizontal symmetry expectation, quark mass matrices turn out to be
not symmetric. Two solutions emerge: one with M_{32}^{{down}}>> M_{23}^{down}}
and M_{21}^{up}>> M_{12}^{{up}}; and a second one with slight asymmetries only
in the light quark sector, namely M_{21}^{up} < M_{12}^{up} and
M_{21}^{down}>M_{12}^{down}.
