  Methods. We use both a Monte Carlo (MC) sampling and a Bayesian analysis to
find the effects of the photospheric composition and the touchdown radius. We
apply these two methods to six LMXBs that show PRE XRBs. In both methods, we
solve the Eddington flux equation and the apparent angular area equation both
of which include the correction terms. For the MC sampling, we have developed
an iterative method in order to solve these two equations more efficiently.
Results. We confirm that the effects of the photospheric composition and the
touchdown radius are similar in the statistical and analytical estimation of
mass and radius even when the correction terms are considered. Furthermore, in
all of the six sources, we find that a H-poor photosphere and a large touchdown
radius are favored statistically regardless of the statistical method. Our
Bayesian analysis also hints that touchdown can occur farther from the neutron
star surface when the photosphere is more H-poor. This correlation could be
qualitatively understood with the Eddington flux equation. We propose a
physical explanation for this correlation between the photospheric composition
and the touchdown radius. Our results show that when accounting for the
uncertainties of the photospheric composition and the touchdown radius, most
likely radii of the neutron stars in these six LMXBs are less than 12.5 km,
which is similar to the bounds for the neutron star radius placed with the
tidal deformability measured from the gravitational wave signal.
