  We continue our systematic statistical study on optical afterglow data of
gamma-ray bursts (GRBs). We present the apparent magnitude distributions of
early optical afterglows at different epochs (t= 10^2 s, t = 10^3 s, and 1
hour) for the optical lightcurves of a sample of 93 GRBs (the global sample),
and for sub-samples with an afterglow onset bump or a shallow decay segment.
For the onset sample and shallow decay sample we also present the brightness
distribution at the peak time t_{p} and break time t_{b}, respectively. All the
distributions can be fit with Gaussian functions. We further perform Monte
Carlo simulations to infer the luminosity function of GRB optical emission at
the rest-frame time 10^3 seconds, t_{p}, and t_{b}, respectively. Our results
show that a single power-law luminosity function is adequate to model the data,
with indices -1.40+/-0.10, -1.06+/- 0.16, and -1.54\+/- 0.22, respectively.
Based on the derived rest-frame 10^3 s luminosity function, we generate the
intrinsic distribution of the R-band apparent magnitude M_{R} at the observed
time 10^{3} seconds post trigger, which peaks at M_{R}=22.5 mag. The fraction
of GRBs whose R-band magnitude is fainter than 22 mag, and 25 mag and at the
observer time 10^3 seconds are ~63% and ~25%, respectively. The detection
probabilities of the optical afterglows with ground-based robotic telescopes
and UVOT onboard {Swift} are roughly consistent with that inferred from this
intrinsic M_{R} distribution, indicating that the variations of the dark GRB
fraction among the samples with different telescopes may be due to the
observational selection effect, although the existence of an intrinsically dark
GRB population cannot be ruled out.
