tokens: al. ( 2013 ), blue circles of Fig. 2 and Magnelli et al. ( 2011 ), red circles of Fig. 2 . The parameters of the analytic expression (dark green dot–dashed line) we obtain from dust correcting the Schechter ( 1976 ) fit given by Cucciati et al. ( 2012 ) are φ ⋆ = 0.0033 Mpc −3 , SFR ⋆ = 16.7 M ⊙ yr −1 and α = −1.07. 3.7 The star formation rate function at <italic>z</italic> ∼ 1.15 To obtain an estimate of the SFRF at redshift z ∼ 1.15, we use the IR LFs from Gruppioni et al. ( 2013 , z ∼ 1.0–1.2) and Magnelli et al. ( 2013 , z ∼ 1.0–1.3) and the FUV LF of Cucciati et al. ( 2012 , z ∼ 1.0–1.2). Even at these intermediate redshifts, the IR surveys are unable to probe low star-forming objects. The red dashed line is the analytical SFRF obtained from the double power-law fit of the LF of Magnelli et al. ( 2013 ). The results from the FUV LF of Cucciati et al. ( 2012 ) imply a much shallower SFRF with a much lower characteristic SFR. Once again we see that the SFRFs from the extrapolations of IR studies typically have higher characteristic SFRs and are steeper for faint objects than those found by UV data. Our results for the SFRF at redshift z ∼ 1.15 are in the bottom left panel of Fig. 2 and Table 8 . Table 8. Stepwise SFR functions at z ∼ 1.15 using the data from Gruppioni et al. ( 2013 , red diamonds of Fig. 2 ) and Magnelli et al. ( 2013 , red circles in the bottom left panel of Fig. 2 ). The parameters of the analytic expression (dark green dot–dashed line) we obtain from dust correcting the Schechter ( 1976 ) fit given by Cucciati et al. ( 2012 ) are φ ⋆ = 0.006 Mpc −3 , SFR ⋆ = 8.3 M ⊙ yr −1 and α = −0.93. 3.8 The star formation rate function at <italic>z</italic> ∼ 0.9 To retrieve the SFRF at redshift z ∼ 0.9, we use the LFs of Ly et al. ( 2011 , z ∼ 0.84), Gruppioni et al. ( 2013 , ∼0.8–1.0), Cucciati et al. ( 2012 , ∼0.8–1.0), Magnelli et al. ( 2013 , z ∼ 0.7–1.0) and Sobral et al. ( 2013 , z ∼ 0.84). As discussed in Section 2.2 , the LF of Ly et al. ( 2011 ) is an Hα LF that is corrected for incompleteness and dust attenuation effects with the Hopkins et al. ( 2001 ) dust correction law. This dust correction law implies a luminosity/SFR dependent correction with the observed (non-intrinsic) luminosity/SFR. To obtain the SFRF from this Hα LF we use equation ( 2 ). The magenta filled diamonds of Fig. 2 are the stepwise determination of the SFRF for z ∼ 0.84 from the Hα LF of Ly et al. ( 2011 ). From Fig. 2 , we see that the bright end of the SFRF from Ly et al. ( 2011 ) is in excellent agreement with the results from the IR samples and this suggests that the SFR dependent dust corrections suggested by Hopkins et al. ( 2001 ) are robust. For the low star-forming objects, we see that the SFRFs derived from Ly et al. ( 2011 ) and Sobral et al. ( 2013 ) are in very good agreement. However, the SFRFs that rely on the results of Sobral et al. ( 2013 ) are highly uncertain for luminous star-forming objects and is not consistent with the SFRs of
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