  In a recent paper, a new parametrization for the dark matter (DM) speed
distribution f(v) was proposed for use in the analysis of data from direct
detection experiments. This parametrization involves expressing the logarithm
of the speed distribution as a polynomial in the speed v. We present here a
more detailed analysis of the properties of this parametrization. We show that
the method leads to statistically unbiased mass reconstructions and exact
coverage of credible intervals. The method performs well over a wide range of
DM masses, even when finite energy resolution and backgrounds are taken into
account. We also show how to select the appropriate number of basis functions
for the parametrization. Finally, we look at how the speed distribution itself
can be reconstructed, and how the method can be used to determine if the data
are consistent with some test distribution. In summary, we show that this
parametrization performs consistently well over a wide range of input
parameters and over large numbers of statistical ensembles and can therefore
reliably be used to reconstruct both the DM mass and speed distribution from
direct detection data.
