Distribution functions for column densities lg(N_H∕[cm⁻²]) of the CNM (left), LNM (middle), and WNM (right), derived from Gaussian components in the velocity range − 8 < v_LSR < 8 km s⁻¹. The light and dark blue colors distinguishes distributions for all Sky and |b| > 20°. The green lines show in each case least square Gaussian fits, resulting in log-normal distributions. For the CNM (left panel) we include the distributions of major filamentary USM structures as observed by Kalberla et al. (2016; their Fig. 12). On the right hand side the XNM components are also included for comparison.