Differential column density distribution at 1.9 < z < 3.2 using the Lyα-only fits. Both black (log  N_H i ≥ 12.75) and grey (log  N_H i < 12.75) data points show the results from our quasar sample. The grey data points mark the column densities that are affected by incompleteness. The stars are the data points obtained by Petitjean et al. (1993). The filled circles at log  N_H i > 20.1 and at 19 < log  N_H i < 20.1 are from the SDSS II DR7 at ⟨ z ⟩ = 3.02 by Noterdaeme et al. (2009) and from O’Meara et al. (2007) at ⟨ z ⟩ = 3.1, respectively. The solid line gives the power law fit to our data for log  N_H i = [12.75,14]. The dotted line represent the fit obtained by Hu et al. (1995), while the dashed line represents a theoretical prediction at z ~ 3 by Altay et al. (2011). The vertical error bars indicate 1σ Poisson errors, while the x-axis error bars show the N_H i range covered by each data point. Gas overdensities on the top x-axis are computed using Eq. (10) from Schaye (2001) at z = 2.55 (see text for details).