An electron scattering model which has proved reliable in predicting both characteristic and continuous radiation depth distributions in bulk samples is further developed to cope with the quantification of depth distribution curves in thin films. The validity of the extended model is checked by comprehensive comparisons of calculated emitted x-ray intensities with experimental data. The deviations obtained are generally small, the root-mean-square error being -5%. The results of calculations quantifying the effect of the substrate material on the shape of the depth distribution function in the film are also presented. The curves obtained are discussed in light of known theories and of fundamental physical considerations. The new model generates curves which correspond at least qualitatively with what is to be expected from basic principles and with the results of recent Monte Carlo simulations.