  It has been shown that the observed temporal distribution of transient events
in the cosmos can be used to constrain their rate density. Here we show that
the peak flux--observation time relation takes the form of a power law that is
invariant to the luminosity distribution of the sources, and that the method
can be greatly improved by invoking time reversal invariance and the temporal
cosmological principle. We demonstrate how the method can be used to constrain
distributions of transient events, by applying it to Swift gamma-ray burst data
and show that the peak flux--observation time relation is in good agreement
with recent estimates of source parameters. We additionally show that the
intrinsic time dependence allows the method to be used as a predictive tool.
Within the next year of Swift observation, we find a 50% chance of obtaining a
peak flux greater than that of GRB 060017 -- the highest Swift peak flux to
date -- and the same probability of detecting a burst with peak flux > 100
photons s^{-1} cm^{-2} within 6 years.
