  Fast radio bursts (FRBs) are extremely powerful sources of radio waves
observed at cosmological distances. We use a sophisticated model of FRB
observations -- presented in detail in a companion paper -- to fit FRB
population parameters using large samples of FRBs detected by ASKAP and Parkes,
including seven sources with confirmed host galaxies. Our fitted parameters
demonstrate that the FRB population evolves with redshift in a manner
consistent with, or faster than, the star-formation rate (SFR), ruling out a
non-evolving population at 99.9\% C.L. Our estimated maximum FRB energy is
$\log_{10} E_{\rm max} [{\rm erg}] = 41.84_{-0.18}^{+0.49}$ (68\% C.L.)
assuming a 1\,GHz emission bandwidth, with slope of the cumulative luminosity
distribution $\gamma=-1.16_{-0.12}^{+0.11}$. We find a log-mean host DM
contribution of $145_{-60}^{+64}$\,pc\,cm$^{-3}$ on top of a typical local (ISM
and halo) contribution of $\sim80$\,pc\,cm$^{-3}$, which is higher than most
literature values. These results are consistent with the model of FRBs arising
as the high-energy limit of magnetar bursts, but allow for FRB progenitors that
evolve faster than the SFR.
