  The neutrino sector of a seesaw-extended Standard Model is investigated under
the anarchy hypothesis. The previously derived probability density functions
for neutrino masses and mixings, which characterize the type I-III seesaw
ensemble of $N\times N$ complex random matrices, are used to extract
information on the relevant physical parameters. For $N=2$ and $N=3$, the
distributions of the light neutrino masses, as well as the mixing angles and
phases, are obtained using numerical integration methods. A systematic
comparison with the much simpler type II seesaw ensemble is also performed to
point out the fundamental differences between the two ensembles. It is found
that the type I-III seesaw ensemble is better suited to accommodate
experimental data. Moreover, the results indicate a strong preference for the
mass splitting associated to normal hierarchy. However, since all permutations
of the singular values are found to be equally probable for a particular mass
splitting, predictions regarding the hierarchy of the mass spectrum remains out
of reach in the framework of anarchy.
