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We characterize the intrinsic properties of any FRB using its redshift z , spectral index α and energy E 33 in units of |$10^{33} \, {\rm J}$| emitted across 2128–2848 MHz in the FRB's rest frame. Provided that z is inferred from the measured extra-galactic dispersion measure DM Ex, the fluence F of the observed event defines a track in (α, E 33) space which we refer to as the 'energy track'. Here, we consider the energy tracks for a sample of 254 non-repeating low dispersion measure FRBs from the CHIME/FRB catalogue-1, and use these to determine the conditional energy distribution, n (E 33∣α), i.e. the number of FRBs in the interval Δ E 33 given a value of α. For all values of α, we can identify two distinct energy ranges indicating that there are possibly two distinct FRB populations. At high energies, the distribution is well fitted by a modified Schechter function whose slope and characteristic energy both increase with α. At low energies, the number of FRBs are in excess of the predictions of the modified Schechter function indicating that we may have a distinctly different population of low-energy FRBs. We have checked that our main findings are reasonably robust to the assumptions regarding the Galactic Halo and Host galaxy contributions to the dispersion measure. [ABSTRACT FROM AUTHOR]

Assuming that Fast Radio Bursts (FRBs) are of extragalactic origin, we have developed a formalism to predict the FRB detection rate and the redshift distribution of the detected events for a telescope with given parameters. We have adopted FRB 110220, for which the emitted pulse energy is estimated to be E0 =5.4×1033 J, as the reference event. The formalism requires us to assume models for (a) pulse broadening due to scattering in the ionized intergalactic medium - we consider two different models for this, (b) the frequency spectrum of the emitted pulse - we consider a power-law model Ev αv -α with -5 ≤ α ≤ 5, and (c) the comoving number density of the FRB occurrence rate n(E, wi, z) - we ignore the z dependence and assume a fixed intrinsic pulse width wi = 1 ms for all the FRBs. The distribution of the emitted pulse energy E is modelled through (a) a delta function where all the FRBs have the same energy E = E0, and (b) a Schechter luminosity function where the energies have a spread around E0. The models are all normalized using the four FRBs detected by Thornton et al. Our model predictions for the Parkes telescope are all consistent with the inferred redshift distribution of the 14 FRBs detected there to date. We also find that scattering places an upper limit on the redshift of the FRBs detectable by a given telescope; for the Parkes telescope, this is z ∼ 2. Considering the upcoming Ooty Wide Field Array, we predict an FRB detection rate of ∼0.01 to ∼103 d-1. [ABSTRACT FROM AUTHOR]