  We examine the width of the gamma-ray burst luminosity function through the
distribution of GRB peak fluxes as detected by the Pioneer Venus Orbiter (PVO)
and the Burst and Transient Source Experiment (BATSE). The strength of the
analysis is greatly enhanced by using a merged catalog of peak fluxes from both
instruments with good cross-calibration of their sensitivities. The range of
peak fluxes is increased by approximately a factor of 20 relative to the BATSE
catalog. Thus, more sensitive investigations of the $\log N-\log P$
distribution are possible. We place constraints on the width of the luminosity
function of gamma-ray bursts brighter than the BATSE completeness limit by
comparing the intensity distribution in the merged catalog with those produced
by a variety of spatial density and luminosity functions. For the models
examined, $90\%$ of the {\em detectable\/} bursts have peak luminosities within
a range of 10, indicating that the peak luminosities of gamma-ray bursts span a
markedly less wide range of values than many other of their measurable
properties. We also discuss for which slopes of a power-law luminosity function
the observed width is at the upper end of the constrained range. This is
important in determining the power-law slopes for which luminosity-duration
correlations could be important.

Astrophysics