Flux density cumulative distributions in the optical (R , solid red line), X-ray (at 3 keV, solid blue line) computed at 11 h after the start of the GRB emission for the BAT6 Swift complete sample (adapted from Melandri et al. 2014; and D’Avanzo et al. 2012, for the optical and X-ray band, respectively). The radio (at 8.4 GHz – solid green line) is from Ghirlanda et al. (2013b), also for the BAT6 sample. The results of the population synthesis code with p = 2.3,ϵ_e = 0.02 and ϵ_B = 0.008 are shown with the dashed lines. The shaded regions represent, for each band, the results obtained with (p,ϵ_e,ϵ_B) = (2.3,0.01,0.001) for the lower boundary and (p,ϵ_e,ϵ_B) = (2.3,0.05,0.01) for the upper boundary. The X-ray and R band fluxes of the Swift BAT6 sample (solid blue and red line respectively) have been corrected for absorption (D’Avanzo et al. 2012; Campana et al. 2012) and for dust extinction (Melandri et al. 2014; Covino et al. 2013), respectively.