  Fast radio bursts (FRBs) are extremely strong radio flares lasting several
micro- to milliseconds and come from unidentified objects at cosmological
distances, most of which are only seen once. Based on recently published data
in the CHIME/FRB Catalog 1 in the frequency bands 400-800 MHz, we analyze 125
apparently singular FRBs with low dispersion measure (DM) and find that the
distribution of their luminosity follows a lognormal form according to
statistical tests. In our luminosity measurement, the FRB distance is estimated
by using the Macquart relation which was obtained for 8 localized FRBs, and we
find it still applicable for 18 sources after adding the latest 10 new
localized FRBs. In addition, we test the validity of the luminosity
distribution up to the Macquart relation and find that the lognormal form
feature decreases as the uncertainty increases. Moreover, we compare the
luminosity of these apparent non-repeaters with that of the previously observed
10 repeating FRBs also at low DM, noting that they belong to different
lognormal distributions with the mean luminosity of non-repeaters being two
times greater than that of repeaters. Therefore, from the two different
lognormal distributions, different mechanisms for FRBs can be implied.
