Comparison of the Parkes and FAST FRB DM Distribution
  We model the Fast Radio Burst (FRB) dispersion measure (DM) distribution for
the Five-hundred-meter Aperture Spherical Telescope (FAST) and compare this
with the four FRBs published in the literature to date. We compare the DM
distribution of Parkes and FAST, taking advantage of the similarity between
their multibeam receivers. Notwithstanding the limited sample size, we observe
a paucity of events at low DM for all evolutionary models considered, resulting
in a sharp rise in the observed cumulative distribution function (CDF) in the
region of $1000\lesssim\mathrm{DM}\lesssim2000$ pc cm$^{-3}$. These traits
could be due to statistical fluctuations ($0.12 \le p \le 0.22$), a complicated
energy distribution or break in an energy distribution power law, spatial
clustering, observational bias or outliers in the sample (e.g., an excessive
DM_${HOST}$ as recently found for FRB 20190520B). The energy distribution in
this regime is unlikely to be adequately constrained until further events are
detected. Modelling suggests that FAST may be well placed to discriminate
between redshift evolutionary models and to probe the helium ionisation signal
of the IGM.
