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.
