  We investigate the cosmological evolution of 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 non-parametric statistical techniques to account for these
effects, and use these methods to estimate the true distribution of the peak of
the nu F_nu spectrum, E_p, from the raw distribution. The distributions are
obtained from four channel data and therefore are rough estimates. Here, 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 population
of high E_p bursts that are not detected by BATSE, 2) We find a GRB co-moving
rate density quite different from that of other extragalactic objects; in
particular, it is different from the recently determined star formation rate.
