Short gamma-ray bursts (sGRBs) data

First, we derive the Ep-Lp correlation using 16 sGRBs with redshift measurements and determine the pseudo redshifts of 284 Fermi sGRBs. Then, we use the Lynden-Bell c^-^ method to study the luminosity function and formation rate of sGRBs without any assumptions.

A strong evolution of luminosity L(z){propto}(1+z)^4.47^ is found. After removing this evolution, the luminosity function is {Psi}(L){propto}L_0_^-0.29+/-0.01^ for dim sGRBs and {psi}(L){propto}L_0_^-1.07+/-0.01^ for bright sGRBs, with the break point 8.26x10^50^erg/s. We also find that the formation rate decreases rapidly at z<1.0, which is different from previous works.