  We present a general statistical analysis of Gamma Ray Bursts embedded in a
host population. If no host generates more than one observed burst, then we
show that there is a model independent lower bound on the number of hosts, $H$,
of the form $H > c B^2$, where B is the number of observed bursts, and $c$ is a
constant of order one which depends on the confidence level (CL) attached to
the bound. An analysis by Tegmark et al. (1996) shows that the BATSE 3B catalog
of 1122 bursts is consistent with no repeaters being present, and assuming that
this is indeed the case, our result implies a host population with at least
H=1.2x10^6 members. Without the explicit assumption of no repeaters, a Bayesian
analysis based on the results of Tegmark et al. (1996) can be performed which
gives the weaker bound of $H>1.7\times 10^5$ at the 90% CL. In the light of the
non-detection of identifiable hosts in the small error-boxes associated with
transient counterparts to GRBs, this result gives a model independent lower
bound to the number of any rare or exotic hosts. If in fact GRBs are found to
be associated with a particular sub-class of galaxies, then an analysis along
the lines presented here can be used to place a lower bound on the fraction of
galaxies in this sub-class. Another possibility is to treat galaxy clusters
(rather than individual galaxies) as the host population, provided that the
angular size of each cluster considered is less than the resolution of the
detector. Finally, if repeaters are ever detected in a statistically
significant manner, this analysis can be readily adapted to find upper and
lower limits on $H$.
