Black dots show the distributions obtained from our Fermi/GBM and Swift SBAT4 samples (Sect. 2). Horizontal error bars are the bin widths, while vertical error bars are 1σ errors on the bin heights accounting for experimental errors on single measurements. The results of our Monte Carlo population synthesis code are shown by solid red lines (assuming E_p−L_iso and E_p−E_iso correlations to hold in the population of SGRBs) and by triple dot-dashed orange lines (assuming no correlation). Predictions based on the models of D14 and WP15 are shown by dashed blue and dot-dashed cyan lines, respectively (the latter only in the first three panels; see text). These are obtained by the analytical methods of Sect. 3.1. Top left panel: distribution of the peak flux P of the Fermi/GBM sample. Top right panel: normalized cumulative redshift distribution of the SBAT4 sample. The grey shaded area represents the range spanned by the distribution if the remaining bursts with unknown z are assigned the largest or the lowest z of the sample. The inset shows the cumulative distributions of the isotropic luminosity L_iso (solid black line) and energy E_iso (solid grey line) of the same sample. Bottom panels: from left to right, distributions of peak energy E_p,o, fluence, and duration of SGRBs of our Fermi/GBM sample.