Radial velocity and proper motion distributions for Regions A to D. The left panels show the radial velocity (v_gsr) distributions of the different regions. The magenta lines in the individual panels represent the best-fit radial velocity distributions (arbitrary vertical scale; see Section 3.3 for details). The red and blue lines mark the contributions of the stream and the background/foreground MW stars, respectively. The dashed green lines represent the radial velocity distributions (arbitrary vertical scale) from the simulated foreground/background MW stars, obtained from the Besançon model (Robin et al. 2003). The red dashed lines represent the radial velocity cut (i.e., ﹩| {v}_{\mathrm{gsr}}-{v}_{\mathrm{gsr}}^{\mathrm{st}}| \leqslant 3{\sigma }_{\mathrm{gsr}}^{\mathrm{st}}﹩) used to select more probable candidates. The middle and right panels show the number distributions of proper motions in the α and δ, respectively. The red histograms in both panels show the distributions after applying the radial velocity cuts.