Abstract
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 ($DM_host$) distribution (a fixed and a random
$DM_host$) are found to predict comparable results. We obtain the best
fit parameter values $\alpha=-1.53^+0.29_-0.19$,
$E_33=1.55^+0.26_-0.22$ and $\gamma=0.770.24$. Here
$\alpha$ is the spectral index, $\gamma$ is the exponent of the Schechter
luminosity function and $E_33$ is the mean FRB energy in units of
$10^33 \, J$ across $2128 - 2848\; MHz$ in the FRB rest frame.
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