**2.12. V / V_{max}, Count and Peak Flux
Distributions**

The limiting fluence observed by BATSE is
10^{-7}
ergs/cm^{2}. The actual fluence of the strongest bursts is
larger by two or three orders of magnitude. A plot of the number of
bursts vs. the peak flux depicts clearly a paucity of weak bursts.
This is manifested by the low value of
<*V* / *V*_{max}>, a
statistic designed to measure the distribution of sources in space
[177].
A sample of the first 601 bursts has
<*V* / *V*_{max}> = .328 ± 0.012, which is
14 away from the
homogeneous flat space value of 0.5
[178].
Correspondingly, the peak count distribution is incompatible with a
homogeneous population of sources in Euclidean space. It is compatible,
however, with a cosmological distribution (see
Fig. 10). The
distribution of short bursts has a larger
<*V* / *V*_{max}>
and it is compatible with a homogeneous Eucleadian distribution
[77,
78,
79].