2003ApJ...593..941Y

The <V/V_max> of the cosmological X-ray flashes detected by the Wide Field Cameras on BeppoSAX is calculated theoretically in a simple jet model. The total emission energy from the jet is assumed to be constant. We find that if the jet opening half-angle is smaller than 0.03 radian, the theoretical <V/V_max> for fixed opening half-angle is less than ∼0.4, which is consistent with the recently reported observational value of 0.27±0.16 at the 1σ level. This suggests that the off-axis gamma-ray burst jet with the small opening half-angle at the cosmological distance can be identified as the cosmological X-ray flash.