Probability density functions (PDFs) of velocity increments Δv at two separations within the scaling regime, computed from 1 154 634 increments. Top: 49 h⁻¹ Mpc (α = 1.6, β = −0.10, σ = 3.45). Bottom: 439 h⁻¹ Mpc (α = 2.0, β = 0.035, σ = 7.4). The blue points represent the empirical PDFs, while the red curves show the best-fit Lévy-stable distributions. At small separations, the PDFs display pronounced non-Gaussian heavy tails and a slight negative skewness. At larger separations, the stability parameter approaches α → 2, indicating a gradual convergence towards Gaussian statistics, although the empirical distribution still exhibits a broader extreme left tail.