Statistics of cosmological gamma-ray bursts

A phenomenological model of gamma-ray burst spectra is used to calculate the statistics of gamma-ray bursts originating at cosmological distances. A model of bursters with no source evolution in a q sub 0 = 1/2 Friedmann cosmology is in accord with recent observations of the differential V/Vmax distribution. The data are best fit with an average peak-burst luminosity of (4 +/- 2) x 10 exp 51 ergs/s and a present-day source emissivity of 940 +/- 440 bursts/(10 exp 10 yr) cu Mpc. A spectral test of the cosmological hypothesis is proposed.