Left panel: GRB-formation rate (normalised to its peak) for the simulated population of GRBs with flux limit 5 × 10^-8 erg cm^-2 s^-1 (black symbols). The GRB-formation rate assumed in the simulation is shown by the dashed green line. The red symbols show the results obtained from the same sample using, for the analysis, a flux limit factor of 5 smaller than the real one. Blue symbols are obtained by mimicking the sample incompleteness by removing some GRBs randomly near the flux threshold adopted for the sample selection. Right panel: cumulative luminosity function, normalised to the first bin. The black, red, and blue symbols are the same as for the left panel. The assumed luminosity function is shown by the dashed green line.