  Using the BATSE peak flux distribution we rederive the short GRBs luminosity
function and compare it with the observed redshift distribution of long bursts.
We show that both distributions are compatible with the assumption that short
as well as long bursts follow the star formation rate. In this case the
difference between the two observed distributions can be interpreted as arising
mostly from differences in the detector's sensitivity to long and short bursts,
while the local rate of short bursts is 0.1 h_70^3 Gpc^-3 yr^-1 . We also
consider the possibility that short GRBs may be associated with binary neutron
star mergers and estimate the effect of the merging time delay on the
luminosity function and redshift distribution. We find that in this case the
local rate of short GRBs is ~0.8 h_70^3 Gpc^-3 yr^-1. Assuming that all binary
merging systems lead to short GRBs, we find a typical jet opening angle of
1.6^o
