Differential column density distribution (f_H   I(N,z)) plotted against log N_H   I. The red data points indicate f_H   I(N,z) for sub-DLAs from the combined sub-DLA sample. The green filled data points represent f_H   I(N,z) for Lyα forest from Kim et al. (2013). The green open circles are column densities from Kim et al. (2013) affected by incompleteness. The cyan data points represent the results from Noterdaeme et al. (2012). The solid magenta line is the estimate of f_NH   I(N,z) at z ~ 3.7 using a series of six power-laws by Prochaska et al. (2010). The solid orange line is hydrodynamic/analytical model prediction at z ~ 3 by Altay et al. (2011).