  The space- and temperature-dependent electron distribution $n(r,T)$
determines optoelectronic properties of disordered semiconductors. It is a
challenging task to get access to $n(r,T)$ in random potentials, avoiding the
time-consuming numerical solution of the Schr\"{o}dinger equation. We present
several numerical techniques targeted to fulfill this task. For a degenerate
system with Fermi statistics, a numerical approach based on a matrix inversion
and that based on a system of linear equations are developed. For a
non-degenerate system with Boltzmann statistics, a numerical technique based on
a universal low-pass filter and one based on random wave functions are
introduced. The high accuracy of the approximate calculations are checked by
comparison with the exact quantum-mechanical solutions.
