Cumulative distributions of line accretion rate [λ = L_line/L_Edd]. The line accretion rate distributions are divided into four regions that correspond to different accretion discs: (1) λ < λ₁ is the pure advection-dominated accretion flows (ADAFs); (2) λ₁ < λ < λ₂ is the coexistence of the ADAFs and the optically thick and geometrically thin disc; (3) λ₂ < λ < λ₃ is the standard thin disc; (4) λ > λ₃ is the super-Eddington accretion. The upper panel covers 431 low-excitation radio galaxies. The labels are the same as in Fig. 1. The lower panel is for the 75 Fermi BL Lacertae objects. The solid yellow line is for high-synchrotron-peaked BL Lacs (HBLs); the dashed purple line is for intermediate-synchrotron-peaked BL Lacs (IBLs), and the dash-dotted orange line is for low-synchrotron-peaked BL Lacs (LBLs).