log f_0pm vs. log f_0plx distributions of the Good_Sky (left panel) and Good_Mag (right panel), along with the quasar selection regions of the adopted astrometric criteria. The left panel shows the distributions of the sky-unbinned GoodQSO_Sky (blue points) and GoodSTAR_Sky (red points), while the right panel displays the corresponding distributions for the magnitude-unbinned GoodQSO_Mag (blue) and GoodSTAR_Mag (red). The black dotted dashed lines represent the f_0pm criteria, while the dotted ones represent the f_0plx criteria. All the histograms are normalized as probability density distributions (PDFs). Due to the long-tailed distributions of stars in log f_0pm and log f_0plx, i.e., many stars fall outside the plot range, both subplots display only small portions of the entire distributions.