  The statistical approach is used to calculate the parton distribution
functions (PDFs) of the nucleon. At first it is assumed that the partons are
free particles and the light-front kinematic variables are employed to extract
the Bjorken $x$-dependence of the PDFs. These PDFs are used to evaluate the
combinations of the sea quarks such as $\bar d-\bar u$. As our first attempt to
improve the result, we make the statistical parameters to depend on $Q^2$,
using different values of Gottfried sum rule. The related results are
indicating better behavior by accessing to the PDFs while they contain the
$Q^2$ dependence parameters. As a further task and in order to have more
improvement in the calculations, a linear potential is considered to describe
the quark interactions. The solution of the related Dirac equation yields the
Airy function and is considered as a wave function in spatial space. Using the
fourier transformation the wave functions are obtained in momentum space. Based
on the light-front kinematic variables and using a special method which we call
it "k method", these functions can be written in terms of the Bjorken
$x$-variable. Following that the statistical features are accompanied with
these functions. Considering an effective approach which is used in this
article, we do not need to resort to any extra effects as were assumed in some
articles to get a proper results for PDFs. The obtained results for $\bar
d-\bar u$ and the $\frac{\bar d}{\bar u}$ ratio, using our effective approach,
are in good agreement with the available experimental data and some theoretical
results.
