  Using a novel approach, the distribution of fluences of long gamma ray bursts
derived from the Swift-BAT catalog, was reproduced by a jet-model characterized
by the distribution of the total radiated energy in $\gamma$-rays and the
distribution of the aperture angle of the emission cone. The best fit between
simulated and observed fluence distributions permits to estimate the parameters
of the model. An evolution of the median energy of the bursts is required in
order to reproduce adequately the observed redshift distribution of the events
if the formation rate of $\gamma$-ray bursts follows the cosmic star formation
rate. For our preferred model, the median jet energy evolves as $E_J \propto
e^{0.5(1+z)}$ and the mean expected jet energy is $3.0\times 10^{49}$ erg,
which agrees with the mean value derived from afterglow data. The estimated
local formation rate is $R_{grb}=290 Gpc^{-3}yr^{-1}$, representing less than
9% of the local formation rate of type Ibc supernovae. The present result
suggests also that the progenitors of long gamma ray bursts have masses $\geq
90 M_\odot$ if a Miller-Scalo initial mass function is assumed.
