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 ${\mathit{q}}_0$=1/2 Friedmann cosmology is in accord with recent observations of the differential V/${\mathit{V}}_{\max }$ distribution. The data are best fitted with an average peak burst luminosity of 4(±2)×${10}^{51}$ ergs ${\mathrm{s}}^{\mathrm{-}1}$ and a present-day source emissivity of 940±440 bursts/(${10}^{10}$ yr) ${\mathrm{Mpc}}^3$. A spectral test of the cosmological hypothesis is proposed.