We have used the photon spectra of gamma-ray bursts (GRBs) obtained from data from the Large Area Detectors of the Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory to produce cosmological models of the burst number-intensity distribution. Since it has become common to assume a canonical or average burst photon spectrum in computations of this type, we have examined the consequences of this assumption by using a range of observed burst spectra to create theoretical intensity distributions. We used a conventional Friedmann cosmology to create the models, and assumed that there is no burst source rate density evolution and that the sources are monoluminous (standard candles). This enabled us to focus on the effects of spectral shape on the log N-log P model parameters (peak luminosity and redshift); the shape of the burst spectrum is found to have an influence on the maximum redshift consistent with the BATSE data. The use of a canonical burst spectrum in modelling the number-intensity distribution yields results that are moderately dependent upon the assumed spectral shape.

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