Quality of Band fits to GRB spectra from GBM catalogue (Bhat et al. 2016). Left: spectral slopes α (top) and β (bottom) as a function of peak flux for the GBM spectral catalogue (Bhat et al. 2016). The entire catalogue of long GRBs above 0.9 ph s⁻¹ cm⁻² is in light-grey, the bursts complying with the ‘good’ criteria (i.e., small errors on the parameters) are shown in blue, the bursts for which Band is the best-fit spectral model are shown in orange. Right: reduced χ² distribution for Band models from the GBM spectral catalogue (Bhat et al. 2016).