  The relation between the event rate of long Gamma-Ray Bursts at low redshift
and the star formation rate is still controversial, especially in the
low-redshift end. Dong et al. confirmed that the Gamma-Ray Burst rate always
exceeds the star formation rate at low-redshift of z < 1 in despite of the
sample completeness. However, the reason of low-redshift excess is still
unclear. Considering low-luminosity bursts with smaller redshift generally, we
choose three Swift long burst samples and classify them into low- and
high-luminosity bursts in order to check whether the low-redshift excess is
existent and if the excess is biased by the sample size and completeness. To
degenerate the redshift evolution from luminosity, we adopt the non-parametric
method to study the event rate of the two types of long bursts in each sample.
It is found that the high-luminosity burst rates are consistent with the star
formation rate within the whole redshift range while the event rates of
low-luminosity bursts exceed the star formation rate at low redshift of z < 1.
Consequently, we conclude that the low-redshift excess is contributed by the
low-luminosity bursts with possibly new origins unconnected with the star
formation, which is also independent of the sample size and the sample
completeness.
