Cumulative distribution of particle velocity (normalized by u₀) in halo groups of different sizes: n_h = 2, 10, 50, and 100. A Gaussian distribution is expected for velocity of all particles in the same group. The cumulative distribution should be error function. Symbols plot the original data from a large-scale N-body simulation and lines plot the best fitted error function. Simulation data confirm Gaussian distribution of particle velocity in the same group, while the velocity of all the particles in all halos is non-Gaussian (i.e., the X distribution).