  We use a suite of 3D simulations of star-forming molecular clouds, with and
without stellar feedback and magnetic fields, to investigate the effectiveness
of different fitting methods for volume and column density probability
distribution functions (PDFs). The first method fits a piecewise lognormal and
power-law (PL) function to recover PDF parameters such as the PL slope and
transition density. The second method fits a polynomial spline function and
examines the first and second derivatives of the spline to determine the PL
slope and the functional transition density. We demonstrate that fitting a
spline allows us to directly determine if the data has multiple PL slopes. The
first PL (set by the transition between lognormal and PL function) can also be
visualized in the derivatives directly. In general, the two methods produce
fits that agree reasonably well for volume density but vary for column density,
likely due to the increased statistical noise in column density maps as
compared to volume density. We test a well-known conversion for estimating
volume density PL slopes from column density slopes and find that the spline
method produces a better match (\c{hi}2 of 2.38 vs \c{hi}2 of 5.92), albeit
with a significant scatter. Ultimately, we recommend the use of both fitting
methods on column density data to mitigate the effects of noise.
