Surface density of proper motion moduli (defined in Eq. (19)) for the four 5° distant regions around NGC 6397 (for simplicity, we call them SOUTH, EAST, WEST and NORTH), represented by red crosses. Solid green curves display the best MLE fit for a Gaussian distribution, while dashed green curves display the best Gaussian MLE fit when only considering the regions with proper motions inside the limit of the dashed blue vertical line. The best MLE fit using Eq. (18) is displayed as the black curves.