The realization that the total energy of GRBs is correlated with their jet break angles motivates the search for a similar relation between the peak luminosity , L , and the jet break angles , L \propto \theta ^ { -2 } .
Such a relation implies that the GRB luminosity function determines the angular distribution .
We re-derive the GRB luminosity function using the BATSE peak flux distribution and compare the predicted distribution with the observed redshift distribution .
The luminosity function can be approximated by a broken power law with a break peak luminosity of 4.4 \times 10 ^ { 51 } erg/sec , a typical jet angle of 0.12 rad and a local GRB rate of 0.44 h _ { 65 } ^ { 3 } Gpc ^ { -3 } yr ^ { -1 } .
The angular distribution implied by L \propto \theta ^ { -2 } agrees well with the observed one , and implies a correction factor to the local rate due to beaming of 75 \pm 25 ( instead of 500 as commonly used ) .
The inferred overall local GRB rate is 33 \pm 11 h _ { 65 } ^ { 3 } Gpc ^ { -3 } yr ^ { -1 } .
The luminosity function and angle distribution obtained within the universal structured jet model , where the angular distribution is essentially \propto \theta and hence the luminosity function must be \propto L ^ { -2 } , deviate from the observations at low peak fluxes and , correspondingly , at large angles .
The corresponding correction factor for the universal structure jet is \sim 20 \pm 10 .