Tsinghua Univ, Tsinghua Ctr Astrophys, Beijing 100084, Peoples R China
; Univ Alabama, Dept Phys, Huntsville, AL 35899 USA
; NASA, Space Sci Lab, George C Marshall Space Flight Ctr, Huntsville, AL 35812 USA
; Chinese Acad Sci, Inst High Energy Phys, Beijing, Peoples R China
It is known that some observed gamma-ray bursts (GRBs) are produced at cosmological distances and that the GRB production rate may follow the star formation rate. We model the BATSE-detected intensity distribution of long GRBs in order to determine their space density distribution and opening angle distribution. Our main results are: the lower and upper distance limits to the GRB production are z approximate to 0.24 and > 10, respectively; the GRB opening angle follows an exponential distribution and the mean opening angle is about 0.03 radians; and the peak luminosity appears to be a better standard candle than the total energy of a GRB.