The Kolmogorov-Smirnov test for three redshift distributions of long gamma-ray bursts in the Swift Era

We investigate redshift distributions of three long burst samples, with the first sample containing 131 long bursts with observed redshifts, the second including 220 long bursts with pseudo-redshifts calculated by the variability-luminosity relation, and the third including 1194 long bursts with pseudo-redshifls calculated by the lag-luminosity relation, respectively. In the redshift range 0-1 the Kolmogorov-Smirnov probability of the observed redshift distribution and that of the variability-luminosity relation is large. In the redshift ranges 1-2, 2-3, 3-6.3 and 0-37, the Kolmogorov-Smirnov probabilities of the redshift distribution from lag-luminosity relation and the observed redshift distribution are also large. For the GRBs, which appear both in the two pseudo-redshift burst samples, the KS probability of the pseudo-redshift distribution from the lag-luminosity relation and the observed reshift distribution is 0.447, which is very large. Based on these results, some conclusions are drawn： i） the V-Liso relation might be more believable than the τ-Liso relation in low redshift ranges and the τ-Liso relation might be more real than the V-Liso relation in high redshift ranges; ii） if we do not consider the redshift ranges, the τ-Liso relation might be more physical and intrinsical than the V-Liso relation.