  The probability density functions (pdfs) of molecular line centroid velocity
fluctuations and fluctuation differences at different spatial lags are
estimated for several nearby molecular clouds with active internal star
formation. The data consist of over 75,000 $^{13}$CO line profiles divided
among twelve spatially and/or kinematically distinct regions. Although three
regions (all in Mon R2) appear nearly Gaussian, the others show strong evidence
for non-Gaussian, often nearly exponential, centroid velocity pdfs, possibly
with power law contributions in the far tails. Evidence for nearly exponential
centroid pdfs in the neutral HI component of the ISM is also presented, based
on older optical and radio observations. These results are in contrast to pdfs
found in isotropic incompressible turbulence experiments and simulations.
Furthermore, no evidence is found for the scaling of difference pdf kurtosis
with Reynolds number which is seen in incompressible turbulence, and the
spatial distribution of high-amplitude velocity differences shows little
indication of the filamentary appearance predicted by decay simulations
dominated by vortical interactions. The variation with lag of the difference
pdf moments is presented as a constraint on future simulations.
