The [Mg/Fe] distribution of metal-rich halo stars with −1 < [Fe/H], The red solid line shows the estimated density based on a Gaussian mixture model (GMM) with three components, while the dashed line shows the density based on a Gaussian kernel density estimation (KDE) with bandwidths of 0.03 dex. Three peaks, corresponding to the α-rich population and the two α-poor sub-populations, are clearly visible in both density estimations.