Comparison between marginal probability densities of shell-crossing times (top left), curvature (top right), C-S transition scale (bottom left), and axis-length ratio (bottom right) measured within the pancake population in 1-LPT simulations initialized using Gaussian random field with the parameters n = 1, R_c = 10 (shown in step histograms) and those computed using Monte Carlo integration of Eq. (44) and transformation through Eqs. (47), (48), (51), and (54) for the same set of parameters (n, R_c) (shown in interpolated curves).