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We use a new method of analysis to determine parameters of cosmological gamma-ray bursts (GRBs), assuming that their distribution follows the star-formation history of the universe. Spectral evolution is calculated from the fireball/blast wave model, and used to evaluate the measured peak flux, duration, and $\nu F_\nu$ peak photon energy for a GRB source occuring at a given redshift and with given values of total energy, baryon-loading and environmental parameters. We then fit model distributions of GRB sources to the observed peak-flux size, duration and $\nu F_\nu$ peak photon energy distributions. Implications for parameters and source models of GRBs are discussed. The ability of the blast wave model to reproduce the three observed GRB distributions self-consistently and simultaneously yields strong support for the external shock model of GRBs, and is in accord with the scenario where GRBs originate from events involving the collapse of massive stars

A New Approach to Statistics of Cosmological Gamma‐Ray Bursts