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

Velocity Field Statistics in Star‐forming Regions. I. Centroid Velocity Observations