  We investigate the parton-distribution functions (PDFs) for the positively
charged pion and kaon at a low-renormalization scale ~ 1 GeV. To this end, we
employ the gauge-invariant effective chiral action from the nonlocal
chiral-quark model, resulting in that the vector currents are conserved. All
the model parameters are determined phenomenologically with the normalization
condition for PDF and the empirical values for the pseudoscalar-meson
weak-decay constants. We consider the momentum dependence of the effective
quark mass properly within the model calculations. It turns out that the
leading local contribution provides about 70 % of the total strength for PDF,
whereas the nonlocal one that is newly taken into account in this work for the
gauge invariance does the rest. High-Q^2 evolution to 27 GeV^2 is performed for
valance-quark distribution function (VQDF), using the DGALP equation. The
moments for the pion and kaon VQDFs are also computed. The numerical results
are compared with the empirical data and theoretical estimations, and show
qualitatively agreement with them.
