Resulting distributions after changing our model to incorporate the MZR of Kobulnicky & Kewley (2004) instead of the MZR of Sanders et al. (2021), showing results for Z_th = 8.3, 8.6, and 8.8 as well as no threshold at all (dark blue, blue, light blue, and red, respectively) and κ = 5 and 20 (left and right column, respectively). The higher value of κ corresponds to a sharper cutoff in η_LGRB (see Eq. (16) and Fig. 4). The red line with no implemented threshold traces the SFR distribution. We compare the simulation to the rate estimate of Ghirlanda & Salvaterra (2022), the host galaxy masses listed in Appendix A, and the KK04 metallicity estimates of Graham et al. (2023), see Fig. 7 for more details. The latter two distributions were bootstrapped and scattered in order to account for the limited sample size and observational uncertainty (as described in Sect. 3), where in the bottom row we use the median uncertainty (i.e. 0.21) for the data points with no listed uncertainty. The light grey areas show the 95% confidence intervals.