Changes in spectral distribution of oscillator strength for core-to-valence transitions probed by X-ray absorption and total electron yield (TEY) modes are studied in more detail. The quantitative analysis of their redistribution in TEY due to the saturation effect is performed by applying the model M $\tilde M$-function method suggested by Flesch et al. J. Chem. Phys. 138 (2013) 144302. The model M $\tilde M$-function method is generalized to account for the saturation-induced distortion of the line shape of the transitions embedded into the core ionization continua and located below them. It is shown that TEY measurements produce essential changes not only in the relative intensity of the transitions but also shift upward the transition energy, broaden the Lorentzian and Gaussian widths and enhance the line asymmetry. The Gaussian width of the TEY signal undergoes the most substantial broadening though the Lorentzian width increases significantly too. The saturation-induced distortion of the line shapes is not negligible even if the well-known escape-to-penetration condition is valid.