The stellar mass distribution of the BGGs and Gaussian approximations are shown as solid black histogram and curve, respectively. The predictions from the SAMs of G11, B06, and DLB07 are shown as the dotted red, dash–dotted blue, and dashed green histograms and curves, respectively. The lower-right panel shows the residual between the observed and the fitted fraction of the BGGs in similar stellar mass bins for S-I, the blue dotted and green dash-dotted lines correspond to the position of the maximum deviation (<log(M_Gd) >) of the observed distribution from the Gaussian distribution and the position of the centre of the peak in the Gaussian distribution (log(M_cen)).