Blue solid histogram with error bars in the top panel: SFR distribution and its uncertainty of z< 2 GRBs, where we have applied the correction for the over-proportionality of dusty GRBs in the sample (Sects. 2.3.3 and 2.4). Black data show all raw measurements without corrections. Lower panel: cumulative distributions of SFR and its uncertainty of z< 0.7 hosts (dark blue), 0.7 <z< 1.3 hosts (olive) and, 1.3 <z< 2.0 hosts (red), in the same way corrected as the blue histogram. The black dashed line denotes hosts at z> 2.