  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.
