[M/H] and [Mg/Fe] distribution functions observed for low-α stars (black histogram) compared with the theoretical distribution functions for the two-infall model including migration prescriptions from Frankel et al. (2018) (cyan line) and corrected for the selection function. The theoretical distribution functions are convoluted with Gaussians with σ_[M/H] and σ_[Mg/Fe] (see Sect. 4.2). The cyan, light blue, and blue shaded regions indicate the contribution from stars born around 4 kpc, 8 kpc, and 12 kpc, respectively.