2018ApJ...858....4N

We investigate how the statistical properties of dispersion measure (DM) and apparent flux density/fluence of (nonrepeating) fast radio bursts (FRBs) are determined by unknown cosmic rate density history [ρ_FRB(z)] and luminosity function (LF) of the transient events. We predict the distributions of DMs, flux densities, and fluences of FRBs taking account of the variation of the receiver efficiency within its beam, using analytical models of ρ_FRB(z) and LF. Comparing the predictions with the observations, we show that the cumulative distribution of apparent fluences suggests that FRBs originate at cosmological distances and ρ_FRB increases with redshift resembling the cosmic star formation history (CSFH). We also show that an LF model with a bright-end cutoff at log₁₀L_ν (erg s^–1 Hz^–1) ∼ 34 are favored to reproduce the observed DM distribution if ρ_FRB(z) ∝ CSFH, although the statistical significance of the constraints obtained with the current size of the observed sample is not high. Finally, we find that the correlation between DM and flux density of FRBs is potentially a powerful tool to distinguish whether FRBs are at cosmological distances or in the local universe more robustly with future observations.