Abstract
We reconstruct the extragalactic dispersion measure – redshift () relation from well-localized fast radio bursts (FRBs) using Bayesian inference. Then, the relation is used to infer the redshift and energy of the first CHIME/FRB catalog. We find that the distributions of the extragalactic dispersion measure and inferred redshift of the non-repeating CHIME/FRBs follow a cut-off power law but with a significant excess at the low-redshift range. We apply a set of criteria to exclude events that are susceptible to the selection effect, but the excess at low redshifts still exists in the remaining FRBs (which we call the gold sample). The cumulative distributions of fluence and energy for both the full sample and the gold sample do not follow the simple power law, but they can be well fitted by the bent power law. The underlying physical implications require further investigation.
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