  We investigate the electron energy distributions (EEDs) and the corresponding
acceleration processes in the jet of PKS 0447$-$439 and estimate its redshift
through modeling its observed spectral energy distribution (SED) in the frame
of a one-zone synchrotron-self Compton (SSC) model. Three EEDs formed in
different acceleration scenarios are assumed: the power-law with exponential
cut-off (PLC) EED (shock-acceleration scenario or the case of the EED
approaching equilibrium in the stochastic-acceleration scenario), the
log-parabolic (LP) EED (stochastic-acceleration scenario and the acceleration
dominating) and the broken power law (BPL) EED (no acceleration scenario), and
then the corresponding fluxes of both synchrotron and SSC are calculated. The
model is applied to PKS 0447-439 and modeling SEDs are compared to the observed
SED of this object by using the Markov Chain Monte Carlo (MCMC) method.
Calculating results show that PLC model fails to fit the observed SED well,
while the LP and BPL models give comparably good fits for the observed SED. The
results indicate that it is possible that stochastic acceleration process acts
in the emitting region of PKS 0447-439 and the EED is far from equilibrium
(acceleration dominating) or no acceleration process works (in the emitting
region). The redshift of PKS 0447-439 is also estimated in our fitting, and
$z=0.16\pm0.05$ for LP case and $z=0.17\pm0.04$ for BPL case.
