Taking into account that a proper description of disordered systems should focus on
distribution functions, the authors develop a powerful numerical scheme for the determination
of the probability distribution of the local density of states (LDOS), which is based
on a Chebyshev expansion with kernel polynomial refinement and allows the study of
large finite clusters (up to \(100^3\)). For the three-dimensional Anderson model it
is demonstrated that the distribution of the LDOS shows a significant change at the
disorder induced delocalisation-localisation transition. Consequently, the so-called
typical density of states, defined as the geometric mean of the LDOS, emerges as a
natural order parameter. The calculation of the phase diagram of the Anderson model
proves the efficiency and reliability of the proposed approach in comparison to other
localisation criteria, which rely, e.g., on the decay of the wavefunction or the inverse
participation number.