  The data from all observations of RX J0720.4-3125 conducted by XMM-Newton
EPIC-pn with the same instrumental setup in 2000-2012 were reprocessed to form
a homogenous data set of solar barycenter corrected photon arrival times
registered from RX J0720.4-3125. A Bayesian method for the search, detection,
and estimation of the parameters of an unknown-shaped periodic signal was
employed as developed by Gregory & Loredo (1992).
  A number of complex models (single and double peaked) of light curves from
pulsating neutron stars were statistically analyzed. The distribution of phases
for the registered photons was calculated by folding the arrival times with the
derived spin-period and the resulting distribution of phases approximated with
a mixed von Mises distribution, and its parameters were estimated by using the
Expected Maximization method. Spin phase-resolved spectra were extracted, and a
number of highly magnetized atmosphere models of an INS were used to fit
simultaneously, the results were verified via an MCMC approach. The
phase-folded light curves in different energy bands with high S/N ratio show a
high complexity and variations depending on time and energy.
  They can be parameterized with a mixed von Mises distribution, i.e. with
double-peaked light curve profile showing a dependence of the estimated
parameters (mean directions, concentrations, and proportion) upon the energy
band, indicating that radiation emerges from at least two emitting areas.
  The genuine spin-period of the isolated neutron star RX J0720-3125 derived as
more likely is twice of that reported in the literature (16.78s instead of
8.39s).
  The gravitational redshift of RX J0720.4-3125 was determined to
$z=0.205_{-0.003}^{+0.006}$ and the compactness was estimated to
$(M/M_{Sun})/R(km)=0.105 \pm 0.002 $.
