  We propose a sampling method to include the negative contribution to
probability density distribution in a sampling procedure. This sampling method
is a universal solution for all negative probability problem and shows
extraordinarily power in negative cross section problem. A Monte Carlo
simulation including negative cross section contribution is developed and
successfully preformed to simulate reflection electron energy loss spectroscopy
(REELS) spectra for Ag and Au as examples. Excellent agreement is found between
simulated spectra and experimental measurements. Notably improved fits to
experimental REELS spectra in low energy loss range illustrate the method's
strength as well as the necessity of negative cross section contribution.
