We constrain the isotropic luminosity function ( LF ) and formation rate of long \gamma -ray bursts ( GRBs ) by fitting models jointly to both the observed differential peak flux and redshift distributions .
We find evidence supporting an evolving LF , where the luminosity scales as ( 1+z ) ^ { \delta } with an optimal \delta of 1.0 \pm 0.2 .
For a single power-law LF , the best slope is \sim -1.57 with an upper luminosity of 10 ^ { 53.3 } erg s ^ { -1 } , while the best slopes for a double power-law LF are approximately -1.6 and -2.6 with a break luminosity of 10 ^ { 52.7 } erg s ^ { -1 } .
Our finding implies a jet model intermediate between the universal structured \epsilon ( \theta ) \propto \theta ^ { -2 } model and the quasi-universal Gaussian structured model .
For the uniform jet model our result is compatible with an angle distribution between 2 ^ { \circ } and 15 ^ { \circ } .
Our best constrained GRB formation rate histories increase from z=0 to z=2 by a factor of \sim 30 and then continue increasing slightly .
We connect these histories to that of the cosmic star formation history , and compare with observational inferences up to z \sim 6 .
GRBs could be tracing the cosmic rates of both the normal and obscured star formation regimes .
We estimate a current GRB event rate in the Milky Way of \sim 5 10 ^ { -5 } yr ^ { -1 } , and compare it with the birthrate of massive close WR+BH binaries with orbital periods of hours .
The agreement is rather good suggesting that these systems could be the progenitors of the long GRBs .