  We study the properties of short gamma-ray bursts (GRBs), based on the
assumption that they are all connected to the binary neutron star mergers,
whose formation mechanism contains a large amount of uncertainty. In
particular, the merger time distribution is focused on, which is essential for
short GRB rate estimate; we simply parameterize it as P_m(t)\propto t^\alpha
with lower cutoff time-scale \tau. The short GRB rate, calculated using such a
parameterization with a specific model of cosmic star formation rate, is found
to be quite insensitive to the value of \tau, but considerably sensitive to
\alpha. With such formation rate models, the peak flux distribution observed by
BATSE is fitted. In the fitting process, the local short GRB rate \rho_0 is
treated as one of free parameters, giving the best fit when \rho_0 = 0.1--2
yr^{-1} Gpc^{-3}, depending on the other free parameters as well as the
formation rate model represented by (\tau,\alpha). We also discuss several
implications for the intrinsic properties of possible sources of short GRBs,
such as jet structure, intrinsic luminosity function, and intrinsic duration
distribution.
