All-sky rate of LGRBs at z ≥ 6, as a function of limiting peak flux for different energy bands in the intrinsic E_p − L correlation scenario. Each panel corresponds to a luminosity evolution scenario (from no evolution at k_evol = 0 to strong evolution at k_evol = 2). To obtain the actual observed rate for a given mission, one should take into account the field of view of the instrument and its duty cycle. The shaded area represents the 95% confidence interval.