A Simultaneous Spectral Invariant Analysis of the GRB Count Distribution and Time Dilation

The analysis of the BATSE's count distribution within cosmological models suffers from observational uncertainties due to the variability of the bursts' spectra: when BATSE observes bursts from different redshifts at a fixed energy band it detects photons from different energy bands at the source. This adds a spectral dependence to the count distribution $N(C)$. Similarly variation of the duration as a function of energy at the source complicates the time dilation analysis. We describe here a new statistical formalism that performs the required ``blue shifting" of the count number and the burst duration in a statistical manner. This formalism allows us to perform a combined best fit (maximal likelihood) to the count distribution, $N(C)$, and the duration distribution simultaneously. The outcome of this analysis is a single best fit value for the redshift of the observed bursts.