Comparison between the predicted |z_max| distributions by the ES21 model (filled histograms) with APOGEE+astroNN stars (empty histograms) for the whole stellar sample introduced in Sect. 2 (left panels), for the high-α sequence (middle panels), and for the low-α sequence (right panels) normalised to the maximum number of stars in the bins of the distributions. In the first row we report ES21 predictions using the vertical action J_z reported in Eq. (3) without including any errors. In the second row, we report ES21 model results, adding a random error normally distributed around J_z with standard deviation σ_Jz fixed at the values of σ_Jz = 0.5 ⋅ J_z. Finally, in the last row the case with σ_Jz = 1 ⋅ J_z is drawn. In each panel, the vertical solid green and dashed black lines indicate the median values of APOGEE stars and model predictions, respectively.