  The statistical properties of overlap sums of groups of four eigenfunctions
of the Anderson model for localization as well as combinations of four
eigenenergies are computed. Some of the distributions are found to be scaling
functions, as expected from the scaling theory for localization. These enable
to compute the distributions in regimes that are otherwise beyond the
computational resources. These distributions are of great importance for the
exploration of the Nonlinear Schr\"odinger Equation (NLSE) in a random
potential since in some explorations the terms we study are considered as noise
and the present work describes its statistical properties.
