Eddington ratio distribution given by Eq. (12) for SMBHs of mass M = 10⁸M_⊙ at different redshifts (black solid lines; dotted lines are for type-1 AGN and dashed lines for type-2 AGN). The Eddington ratio distributions from Kelly & Shen (2013) with an arbritary normalization are also shown (red lines): the two lines give the uncertainty in their estimates (at 68% of probability); dotted lines denote the regions below the 10% completeness for the flux-limited SDSS sample.