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 $gamma=0.77pm 0.24$. 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.
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