Luminosity cumulative distribution function in four different redshift bins for the intrinsic E_p − L correlation scenario. The full lines correspond to k_evol = 2 and the dashed lines to k_evol = 0. Leftmost panel: entire intrinsic LGRB population, centre left and centre right panels: bursts with and 2.6 ph s⁻¹ cm⁻² respectively. Rightmost panel: same as the centre right panel but adding the observed eBAT6 sample and where each curve was shifted by a constant C for clarity. The shaded area represents the 95% confidence region for the CDF of the observed eBAT6 sample, calculated using bootstrapping (without taking into account limits).