  Fast Radio Bursts (FRBs) are the short, strong radio pulses lasting several
milliseconds. They are subsequently identified, for the most part, as emanating
from unknown objects at cosmological distances. At present, over one hundred
FRBs have been verified, classified into two groups: repeating bursts (20
samples) and apparently non-repeating bursts (91 samples). Their origins,
however, are still hotly debated. Here,we investigate the statistical
classifications for the two groups of samples to see if the non-repeating and
repeating FRBs have different origins by employing Anderson-Darling (A-D) test
and Mann-Whitney-Wilcoxon (M-W-W) test. Firstly, by taking the pulse width as a
statistical variant, we found that the repeating samples do not follow the
Gaussian statistics (may belong to a chi-square distribution), although the
overall data and non-repeating group do follow the Gaussian. Meanwhile, to
investigate the statistical differences between the two groups, we turn to
M-W-W test and notice that the two distributions have different origins.
Secondly, we consider the FRB radio luminosity as a statistical variant, and
find that both groups of samples can be regarded as the Gaussian distributions
under the A-D test, although they have different origins according to M-W-W
tests. Therefore, statistically, we can conclude that our classifications of
both repeaters and non-repeaters are plausible, that the two FRB classes have
different origins, or each has experienced distinctive phases or been subject
to its own physical processes.
