Comparison between probability distribution functions of transmitted Lyα forest flux F/F_c as extracted from the reference simulation (red solid), and as predicted by the standard FGPA (yellow dashed), by the FGPA with velocity bias (purple dotted), by the FGPA with velocity and threshold bias (black dashed-dotted), by the nonlocal FGPA(green dashed), and by the nonlocal FGPA and stochasticity (blue dashed-dotted).