  Examining the evolution of the maximum of valence quark distribution weighted
by Bjorken x, $h(x,t)\equiv xq_V(x,t)$, we observe that $h(x,t)$ at the peak
should become a one parameter function; $h(x_p,t)=\Phi(x_p(t))$, where $x_p$ is
the position of the peak and $t= \log{Q^2}$. This observation is used to derive
a new model independent relation which connects the partial derivative of the
valence parton distribution functions (PDFs) in $x_p$ to the QCD evolution
equation through the $x_p$-derivative of the logarithm of the function
$\Phi(x_p(t))$. A numerical analysis of this relation using empirical PDFs
results in a observation of the exponential form of the $\Phi(x_p(t)) =
h(x_p,t) = Ce^{D x_p(t)}$ for leading to next-to-next leading order
approximations of PDFs for the all $Q^2$ range covering four orders in
magnitude. The exponent, $D$, of the observed "height-position" correlation
function converges with the increase of the order of approximation. This result
holds for all PDF sets considered. A similar relation is observed also for pion
valence quark distribution, indicating that the obtained relation may be
universal for any non-singlet partonic distribution. The observed "height -
position" correlation is used also to indicate that no finite number exchanges
can describe the analytic behavior of the valence quark distribution at the
position of the peak at fixed $Q^2$.
