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. In addition, we 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.