  Numerical approaches to Anderson localization face the problem of having to
treat large localization lengths while being restricted to finite system sizes.
We show that by finite-size scaling of the probability distribution of the
local density of states (LDOS) this long-standing problem can be overcome. To
this end we reexamine the approach, propose numerical refinements, and apply it
to study the dependence of the distribution of the LDOS on the dimensionality
and coordination number of the lattice. Particular attention is given to the
graphene lattice. We show that the system-size dependence of the LDOS
distribution is indeed an unambiguous sign of Anderson localization,
irrespective of the dimension and lattice structure. The numerically exact LDOS
data obtained by us agree with a log-normal distribution over up to ten orders
of magnitude and thereby fulfill a nontrivial symmetry relation previously
derived for the non-linear $\sigma$-model.
