  Different forms of long gamma-ray bursts (GRBs) Luminosity Functions are
considered on the basis of an explicit physical model. The inferred flux
distributions are compared with the observed ones from two samples of GRBs,
Swift and Fermi GBM. The best fit parameters of the Luminosity functions are
found and the physical interpretations are discussed. The results are
consistent with the observation of a comparable number of flat phase afterglows
and monotonic decreasing ones.
