The Optical Luminosity Function of Gamma-ray Bursts deduced from   ROTSE-III Observations
  We present the optical luminosity function (LF) of gamma-ray bursts (GRBs) estimated from a uniform sample of 58 GRBs from observations with the Robotic Optical Transient Search Experiment III (ROTSE-III). Our GRB sample is divided into two sub-samples: detected afterglows (18 GRBs), and those with upper limits (40 GRBs). The $R$ band fluxes 100s after the onset of the burst for these two sub-samples are derived. The optical LFs at 100s are fitted by assuming that the co-moving GRB rate traces the star-formation rate. The detection function of ROTSE-III is taken into account during the fitting of the optical LFs by using Monte Carlo simulations. We find that the cumulative distribution of optical emission at 100s is well-described with an exponential rise and power-law decay (ERPLD), broken power-law (BPL), and Schechter LFs. A single power-law (SPL) LF, on the other hand, is ruled out with high confidence. 
X. H. Cui, X. F. Wu, J. J. Wei, F. Yuan, W. K. Zheng, E. W. Liang, C.   W. Akerlof, M. C. B. Ashley, H. A. Flewelling, E. Go...
astro-ph.HE