  Probability distribution functions (PDFs) of column densities are an
established tool to characterize the evolutionary state of interstellar clouds.
Using simulations, we show to what degree their determination is affected by
noise, line-of-sight contamination, field selection, and the incomplete
sampling in interferometric measurements. We solve the integrals that describe
the convolution of a cloud PDF with contaminating sources and study the impact
of missing information on the measured column density PDF. The effect of
observational noise can be easily estimated and corrected for if the root mean
square (rms) of the noise is known. For $\sigma_{noise}$ values below 40% of
the typical cloud column density, $N_{peak}$, this involves almost no
degradation of the accuracy of the PDF parameters. For higher noise levels and
narrow cloud PDFs the width of the PDF becomes increasingly uncertain. A
contamination by turbulent foreground or background clouds can be removed as a
constant shield if the PDF of the contamination peaks at a lower column or is
narrower than that of the observed cloud. Uncertainties in the definition of
the cloud boundaries mainly affect the low-column density part of the PDF and
the mean density. As long as more than 50% of a cloud are covered, the impact
on the PDF parameters is negligible. In contrast, the incomplete sampling of
the uv plane in interferometric observations leads to uncorrectable distortions
of the PDF of the produced maps. An extension of ALMA's capabilities would
allow us to recover the high-column density tail of the PDF but we found no way
to measure the intermediate and low column density part of the underlying cloud
PDF in interferometric observations.
