Mass function of SMBHs (top panel) and AGN (bottom panel) obtained after changing the Eddington ratio distribution. Lines are for following cases: (1) we use a truncated power law for P(λ) of type-1 AGN (red short dashed lines); (2) a power-law distribution for type-2 AGN with constant slope α_λ = −0.6 (black solid lines); (3) a faster evolving power-law distribution (α_λ = −0.6/(0.4 + z)^1.5) for type-2 AGN (green long dashed lines). Shaded areas are for the uncertainty of the model as in Fig. A.2.