The luminosity function (LF) statistics applied to the BATSE GRBs (sources of GUSBAD catalog) is the theme approached in this work. The LF is a strong statistical tool to extract useful information from astrophysical samples, where the key point of this statistical analysis is in the detector sensitivity, where we have performed careful analysis. We applied the tool of the LF statistics to three GRB classes predicted by the Fireshell model. One of the main differences between the Fireshell and Fireball models is the explanation of the GRB prompt emission, where the first claims that it is divided in two physical processes: 1) transparency of a optically thick Freshell producing the P-GRB emission and 2) interaction of a relativistic shell (composed by baryons electron-positron-photon) against the CBM (circumburst medium), producing the emission so-called extended afterglow peak (EAP). However, the Fireball model, the most quoted one, claims that the prompt emission is caused by interactions among several relativistic shells (composed by electron-positron-photon) with different Lorentz factors, a process called internal shocks. The transparency produces a strong short emission in the beginning, called P-GRB. Thus, to the Fireshell model, the prompt emission is P-GRB plus EAP. We produced, by LF statistics, predicted distributions of: peak flux, redshift and peak luminosity for the three GRB classes predicted by Fireshell model, we also used three GRB rates. We looked for differences among the distributions, and in fact we found. We performed a comparison between the distributions predicted and observed (with and without redshifts), where we had to build a list with 220 GRBs with known redshifts. We also estimated the effects of the Malmquist bias in all samples, and we looked for a correlation between the isotropic luminosity and the Band peak spectral energy.

7 pages, 6 figures, 1 table