2003ApJ...584..904M

The small reference sample of six BATSE gamma-ray bursts with known redshifts from optical afterglows is compared with a comparison group of the 218 brightest BATSE bursts. These two groups are shown to be consistent both with respect to the distributions of the spectral peak parameter in the observer's frame and also with respect to the distributions of the frame-independent cosmological invariant parameter (CIP). Using the known values of the redshifts (z) for the reference sample, the rest-frame distribution of spectral parameters is built. The deredshifted distribution of the spectral parameters of the reference sample is compared with distribution of these parameters for the comparison group after deredshifting by the factor 1/(1+z), with z a free parameter. Requiring consistency between these two distributions produces a collective estimation of the best fitting redshifts for the comparison group z=1.8-3.6. These values can be considered as the average cosmological redshift of the sources of the brightest BATSE bursts. The most probable value of the peak energy of the spectrum in the rest frame is 920 keV.