Statistical inference of the distance to ASKAP FRBs
  The distances to fast radio bursts (FRBs) are crucial for understanding their
underlying engine, and for their use as cosmological probes. In this paper, we
provide three statistical estimates of the distance to ASKAP FRBs. First, we
show that the number of events of similar luminosity in ASKAP does not scale as
distance cubed, as one would expect, when directly using the observed
dispersion measure (DM) to infer distance. Second, by comparing the average DMs
of FRBs observed with different instruments, we estimated the average redshift
of ASKAP FRBs to be $z\sim 0.01$ using CHIME and ASKAP, and $z\lesssim0.07$
using Parkes and ASKAP. Both values are much smaller than the upper limit
$z\sim0.3$ estimated directly from the DM. Third, we cross-correlate the
locations of the ASKAP FRBs with existing large-area redshift surveys, and see
a 3$\sigma$ correlation with the 2MASS Redshift Survey and a 5$\sigma$
correlation with the HI Parkes All Sky Survey at $z\sim0.007$. This corresponds
well with the redshift of the most likely host galaxy of ASKAP FRB 171020,
which is at $z=0.00867$. These arguments combined suggest an extremely nearby
origin of ASKAP FRBs and a local environment with accumulated electrons that
contribute a DM of several hundred pc/cm$^3$, which should be accounted for in
theoretical models.
