  Fast radio bursts (FRBs) are usually suggested to be associated with mergers
of compact binaries consisting of white dwarfs (WDs), neutron stars (NSs), or
black holes (BHs). We test these models by fitting the observational
distributions in both redshift and isotropic energy of 22 Parkes FRBs, where,
as usual, the rates of compact binary mergers (CBMs) are connected with cosmic
star formation rates by a power-law distributed time delay. It is found that
the observational distributions can well be produced by the CBM model with a
characteristic delay time from several ten to several hundred Myr and an energy
function index $1.2\lesssim\gamma\lesssim1.7$, where a tentative fixed spectral
index $\beta=0.8$ is adopted for all FRBs. Correspondingly, the local event
rate of FRBs is constrained to $(3-6)\times10^4f_{\rm b}^{-1}(\mathcal T/270\rm
s)^{-1}(\mathcal A/2\pi)^{-1}\rm ~Gpc^{-3}yr^{-1}$ for an adopted minimum FRB
energy of $E_{\min}=3\times10^{39}$ erg, where $f_{\rm b}$ is the beaming
factor of the radiation, $\mathcal T$ is the duration of each pointing
observation, and $\mathcal A $ is the sky area of the survey. This event rate,
about an order of magnitude higher than the rates of NS-NS/NS-BH mergers,
indicates that the most promising origin of FRBs in the CBM scenario could be
mergers of WD-WD binaries. Here a massive WD could be produced since no FRB was
found to be associated with a type Ia supernova. Alternatively, if actually all
FRBs can repeat on a timescale much longer than the period of current
observations, then they could also originate from a young active NS that forms
from relatively rare NS-NS mergers and accretion-induced collapses of WD-WD
binaries.
