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The probability distribution function (PDF) of the mass surface density ofmolecular clouds provides essential information about the structure ofmolecular cloud gas and condensed structures out of which stars may form. Ingeneral, the PDF shows two basic components: a broad distribution around themaximum with resemblance to a log-normal function, and a tail at high masssurface densities attributed to turbulence and self-gravity. In a previouspaper, the PDF of condensed structures has been analyzed and an analyticalformula presented based on a truncated radial density profile, $\rho(r) =\rho_c/(1+(r/r_0)^2)^{n/2}$ with central density $\rho_c$ and inner radius$r_0$, widely used in astrophysics as a generalization of physical densityprofiles. In this paper, the results are applied to analyze the PDF ofself-gravitating, isothermal, pressurized, spherical (Bonnor-Ebert spheres) andcylindrical condensed structures with emphasis on the dependence of the PDF onthe external pressure $p_{ext}$ and on the overpressure $q^{-1} =p_c /p_{ext}$,where $p_c$ is the central pressure. Apart from individual clouds, we alsoconsider ensembles of spheres or cylinders, where effects caused by a variationof pressure ratio, a distribution of condensed cores within a turbulent gas,and (in case of cylinders) a distribution of inclination angles on the mean PDFare analyzed. The probability distribution of pressure ratios $q^{-1}$ isassumed to be given by $P(q^{-1}) \proptoq^{-k_1}/(1+(q_0/q)^{\gamma})^{(k_1+k_2)/{\gamma}}$, where $k_1$, ${\gamma}$,$k_2$, and $q_0$ are fixed parameters.

On the probability distribution function of the mass surface density of molecular clouds. II