  We investigate the ability to discern between lognormal and powerlaw forms
for the observed mass function of dense cores in star forming regions. After
testing our fitting, goodness-of-fit, and model selection procedures on
simulated data, we apply our analysis to 14 datasets from the literature.
Whether the core mass function has a powerlaw tail or whether it follows a pure
lognormal form cannot be distinguished from current data. From our simulations
it is estimated that datasets from uniform surveys containing more than
approximately 500 cores with a completeness limit below the peak of the mass
distribution are needed to definitively discern between these two functional
forms. We also conclude that the width of the core mass function may be more
reliably estimated than the powerlaw index of the high mass tail and that the
width may also be a more useful parameter in comparing with the stellar initial
mass function to deduce the statistical evolution of dense cores into stars.
