  We present results for the nucleon's leading-twist spin-independent valence
parton distribution functions obtained from a theoretical framework based on
the Dyson-Schwinger equations (DSEs) of QCD that previously gave an excellent
description of nucleon electromagnetic form factors. We employ the
rainbow-ladder truncation of the DSEs and utilize nucleon bound state
amplitudes from the Poincar\'e-covariant Faddeev equation, where the dominant
scalar and axial-vector quark-quark correlations are included. This DSE
framework is used to numerically evaluate the first 20 moments of the valence
$u$ and $d$ quark distribution functions, from which the $x$-dependence of the
distributions is found to be well constrained. We find good agreement with
empirical parameterizations of experimental data and make the prediction that
the $d/u$ ratio in the $x\to 1$ limit, invariant under scale evolution, takes
the value $d/u \to 0.087 \pm 0.010$. We find that this ratio is rather
sensitive to the strength of axial-vector diquark correlations. However,
contrary to a naive expectation, our result for the $d/u$ ratio in the $x\to 1$
limit does not vanish when only scalar diquark correlations are present,
although it is an order of magnitude smaller than our $d/u$ result that also
includes axial-vector diquarks. The valence quark distribution results are set
in a broader context via a simple pion cloud model estimate of sea-quark
light-cone momenta and gluon light-cone momentum.
