A maximum-likelihood estimate of the parameters of the fast radio burst population

We consider a sample of 82 non-repeating fast radio bursts (FRBs) detected at Parkes, ASKAP, CHIME, and UTMOST, each of which operates over a different frequency range and has a different detection criterion. Using simulations, we perform a maximum-likelihood analysis to determine the FRB population model that best fits these data. Our analysis shows that models where the pulse scatter broadening increases moderately with redshift (z) are preferred to those where this increases very sharply or where scattering is absent. Further, models where the comoving event rate density is constant over z are preferred to those where it follows the cosmological star formation rate. Two models for the host dispersion measure (DMHost) distribution (a fixed and a random DMHost) are found to predict comparable results. We obtain the best-fitting parameter values $\alpha =-1.53^{+0.29}_{-0.19}$, $\overline{E}_{33}=1.55^{+0.26}_{-0.22}$, and γ = 0.77 ± 0.24. Here α is the spectral index, γ is the exponent of the Schechter luminosity function, and $\overline{E}_{33}$ is the mean FRB energy in units of $10^{33} \, {\rm J}$ across 2128–2848 MHz in the FRB rest frame.