A maximum likelihood estimate of the parameters of the FRB population

We consider a sample of $82$ non-repeating FRBs detected at Parkes, ASKAP, CHIME and UTMOST each of which operates over a different frequency range and has a different detection criteria. Using simulations, we perform a maximum likelihood analysis to determine the FRB population model which best fits this data. Our analysis shows that models where the pulse scatter broadening increases moderately with redshift ($z$) are preferred over 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 over those where it follows the cosmological star formation rate. Two models for the host dispersion measure ($DM_{\rm host}$) distribution (a fixed and a random $DM_{\rm host}$) are found to predict comparable results. We obtain the best fit parameter values $\alpha=-1.53^{+0.29}_{-0.19}$, $\overline{E}_{33}=1.55^{+0.26}_{-0.22}$ and $\gamma=0.77\pm 0.24$. Here $\alpha$ is the spectral index, $\gamma$ 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 $2128 - 2848\; {\rm MHz}$ in the FRB rest frame.