We argue that recent observations of afterglows and some theoretical considerations indicate that the gamma-ray fluence may be a better measure of strength of a burst than its peak flux. We discuss how the distribution of the fluence, or any physical quantity related to the peak counts (or flux), can be obtained with proper correction for threshhold effects. Using this method, we compare the cumulative and differential distributions of flux and fluence. We find some differences between these distributions, but more remarkable are the similarities between these distributions. The other striking feature is how different these distributions are from those of other extragalactic objects. Using the fluence distributions, we derive the expected comoving density rate evolution for different assumed total luminosity; we compare this with the GRB rate expected from the recently determined star formation rate. ©1998 American Institute of Physics.