Histograms of Galactic heights, z; the Galactic-longitude component, v₁; and the Galactic-latitude component, v_b, of transverse peculiar velocities, respectively shown in the left, middle, and right panels. Each histogram is concatenated from 10000 simulations drawn from the assumed split normal distributions for the 64 measurements (of z, v_l, or v_b; see Table B.1). The dashed grey curves show the normalised count smoothed with kernel density estimation (using scipy.stats.Gaussian_kde). The best-fit Cauchy, Laplace and three-component normal distributions are plotted as dashed blue and green curves. The dynamical population synthesis results (labelled as ‘evolved’) that best match the observed z, v₁ and v_b, based on the determined initial MSP scale height of ζ₀=0.32 kpc, are overlaid. The corresponding initial distributions are also provided, except for v₁, as the initial v₁ distribution adopted in the dynamical population synthesis is identical to the best-fit three-component normal distribution (a linear combination of three normal distributions).