N_H   I frequency distribution of DLAs (Péroux et al. 2003b) and sub-DLAs (combined sub-DLA sample) in a range of 1.51 <z< 5.00 is shown as black and red circles, respectively. The Γ-function and double power-law fit to these DLA and sub-DLA results are shown as solid and dashed black lines, respectively. The cyan data points represent the results from Noterdaeme et al. (2012) over two orders of magnitude in N_H   I. The departure at high column densities (log N_H   I> 21.0) from the Γ-function shape is due to low number statistics at higher column density in the former studies.