1999ApJ...511..550L

We investigate the cosmological evolution of gamma-ray bursts (GRBs) using the total gamma-ray fluence as a measure of the burst strength. This involves an understanding of the distributions of the spectral parameters of GRBs, as well as the total fluence distribution–both of which are subject to detector selection effects. We present new nonparametric statistical techniques to account for these effects, and we use these methods to estimate the true distribution of the peak of the νF_ν spectrum–E_p–from the raw distribution. The distributions are obtained from four-channel data, and therefore are rough estimates; hence we emphasize the methods and present qualitative results. Given its spectral parameters, we then calculate the total fluence for each burst and compute its cumulative and differential distributions. We use these distributions to estimate the cosmological rate evolution of GRBs for three cosmological models. Our two main conclusions are the following: (1) given our estimates of the spectral parameters, we find that there may exist a significant number of high-E_p bursts that are not detected by BATSE; and (2) we find a GRB comoving rate density quite different from that of other extragalactic objects–in particular, it is different from the recently determined star formation rate.