A statistical analysis of gamma-ray bursts based on the beaming model

We assume that gamma-ray bursts come from relativistic beaming in random directions, with the bursts being standard candles in their own rest frames and following a power-law distribution, and that the rate of occurrence is a constant in the comoving frame of the Ω = 1, Λ = 0 Friedmann universe. This model is very sensitive to the beaming velocity. For a Lorentz factor Γ < 10 and a power-law index n < 1.0 our calculated statistics agree with the BATSE data of weak bursts and the PVO data of strong bursts.