  In our earlier work on the development of a model-independent data analysis
method for reconstructing the (moments of the) time-averaged one-dimensional
velocity distribution function of Weakly Interacting Massive Particles (WIMPs)
by using measured recoil energies from direct Dark Matter detection experiments
directly, it was assumed that the analyzed data sets are background-free, i.e.,
all events are WIMP signals. In this article, as a more realistic study, we
take into account a fraction of possible residue background events, which pass
all discrimination criteria and then mix with other real WIMP-induced events in
our data sets. Our simulations show that, for the reconstruction of the
one-dimensional WIMP velocity distribution, the maximal acceptable fraction of
residue background events in the analyzed data set(s) of O(500) total events is
~10% - 20%. For a WIMP mass of 50 GeV with a negligible uncertainty and 20%
residue background events, the deviation of the reconstructed velocity
distribution would in principle be ~7.5% with a statistical uncertainty of ~18%
(~19% for a background-free data set).
