Fast radio bursts ( FRBs ) are intense radio transients whose physical origin remains unknown .
Therefore , it is of crucial importance to use a model-independent method to obtain the energy function and cosmic formation rate directly from the observational data .
Based on current samples from the Parkes and ASKAP telecsopes , we determine , for the first time , the energy function and formation rate of FRBs by using the Lynden-Bell C ^ { - } method .
The energy function derived from the Parkes sample is a broken power law , however it is a simple power law for the ASKAP sample .
For Parkes sample , we derive the formation rate which is roughly consistent with the star formation rate up to z \sim 1.7 , with a local formation rate of \dot { \rho } ( 0 ) \simeq ( 3.2 \pm 0.3 ) \times { 10 ^ { 4 } } { Gp } { { c } ^ { -3 } } { % y } { { r } ^ { -1 } } above a detection threshold of 2 { Jyms } .
For ASKAP sample , we find that the formation rate evolves much faster than the star formation rate up to z \sim 0.7 , namely \dot { \rho } ( z ) \propto { ( 1 + z ) ^ { 6.9 \pm 1.9 } } , with a local formation rate of \dot { \rho } ( 0 ) \simeq ( 4.6 \pm 0.8 ) \times { 10 ^ { 3 } } { Gp } { { c } ^ { -3 } } { % y } { { r } ^ { -1 } } above a detection threshold of 51 { Jyms } .
This might be a important clue for the physical origin of FRBs .