The distances of cosmic γ-ray bursts and their distribution

Taking the effect of the expansion of the universe, jet effect and the association of γ-ray bursts with supernovae into consideration, we have studied the space distribution of γ-ray bursts. Assuming a Gaussian distribution of the opening angle and that the rate of bursts is proportional to the rate of star formation, we find the best fitting parameters to be φ0=0.1, and σ=0.04, implying that the opening angles are concentrated about O.1 rad, in agreement with the current analyses on γ-ray bursts with known redshifts. The maximum redshift calculated from 〈 VVmax 〉 is 4.2, and the energy of γ-ray burst is 1.5 × 1051 ergs.