Parent distributions of N_H. Upper panel: parent distributions for a subsample that is the same size as the XMM-COSMOS data sample and is randomly selected from the simulation. The true distribution is plotted as the filled histogram in orange, and the reconstructed N_H distribution obtained by applying FFPI is shown as the black line. The error bars show the 68.3% credible intervals. For comparison, the stacked PDFs, the distributions of medians, and the ML results are plotted in dashed magenta, dashed green, and dash-dotted red lines, respectively. All distributions are normalized to unit area. Lower panel: corner plot of the parameters of the first four bins (p₁ − p₄, converted to probability density for consistency with the lower panel) in the unabsorbed regime.