Best-fit parameters of the maximum-likelihood fitting for p(L_R | M_⋆,  z) of SFGs (blue circles and blue dashed lines), QGs (red squares and red dash-dotted lines), and all galaxies (black stars and black solid lines). The colored symbols represent the best-fit parameters obtained by Eqs. (24)–(27) in each redshift bin (see details in Sects. 6.3.1 and 6.3.2). The colored lines show the best-fit results over the entire redshift range obtained by Eqs. (28)–(29) and (25)–(27) (see details in Sect. 6.3.3). The dotted gray lines represent the results for the X-ray AGNs in Aird et al. (2012).