W.Kirsch and I.Veselić proved a generalized Wegner estimate for Schrödinger operators with generalized alloy type potentials at negative energies for each fixed position of impurities. In this paper, a similar estimate is proven treating also the position of impurities as random variables.
"Wegner estimate for a generalized alloy type potential." J. Math. Kyoto Univ. 49 (2) 255 - 265, 2009. https://doi.org/10.1215/kjm/1256219155