  Kouveliotou et al. (1993) recently confirmed that gamma-ray bursts are
bimodal in duration. In this paper we compute the statistical properties of the
short ($\le 2$~s) and long ($>2$~s) bursts using a method of analysis that
makes no assumption regarding the location of the bursts, whether in the Galaxy
or at a cosmological distance. We find the 64 ms channel on BATSE to be more
sensitive to short bursts and the 1024 ms channel is more sensitive to long
bursts. We show that all the currently available data are consistent with the
simple hypothesis that both short and long bursts have the same spatial
distribution and that within each population the sources are standard candles.
The rate of short bursts is $\sim 0.4$ of the rate of long bursts. Although the
durations of short and long gamma-ray bursts span several orders of magnitude
and the total energy of a typical short burst is smaller than that of a typical
long burst by a factor of $\sim 20$, surprisingly the peak luminosities of the
two kinds of bursts are equal to within a factor of $\sim 2$.
