The intrinsic statistical properties and correlations of short gamma-ray bursts (SGRBs) have not been fully determined, due to the limitations of observations. In this paper, we compile a more extensive sample of 82 SGRBs with measured redshifts and present a comprehensive study of their intrinsic characteristics. We obtain the median values of the intrinsic duration (T90,z), peak energy (Ep,z), isotropic energy (Eiso), and peak luminosity (Liso) as 0.47s, 466keV, 8.21x10^50^erg, and 3.22x10^51^erg/s, respectively. We update the spectrum-energy correlations, and report E_p,z_{propto}E_iso_^0.36+/-0.05^ and E_p,z_{propto}L_iso_^0.33+/-0.04^, which further confirm the previous results that the E_p,z_-E_iso_ correlations of SGRBs and long gamma-ray bursts (LGRBs) are different and that this correlation can be used to distinguish GRB types. We report for the first time that there is a tighter correlation between the isotropic energy of the prompt emission of SGRBs and the star formation rate of their host galaxies, which reads sSFR{propto}E_iso_^0.38+/-0.11^. Using the measured jet break time (t_jet_) of 11 SGRBs, we tentatively investigate the Eiso-E_p,z_-t_jet,z_ and Liso-E_p,z_-t_jet,z_ correlations of SGRBs and find that three-parameter correlations of SGRBs also exist and are different from those of LGRBs. Based on the Eiso-E_p,z_-t_jet,z_ correlation, we estimate the t_jet,z_ values of other SGRBs and calculate the opening angles of SGRBs. We find that the median value of the SGRB opening angle is 7.5{deg}, which is larger than that of LGRBs.

Cone search capability for table J/ApJ/950/30/table1 (The properties of short gamma-ray bursts (SGRBs) in the observed frame)

Cone search capability for table J/ApJ/950/30/table2 (The properties of SGRBs in the rest frame)

Cone search capability for table J/ApJ/950/30/table3 (The properties of long gamma-ray bursts (LGRBs) in the rest frame)