  Focusing on hadron scattering at large partonic momentum fractions $x$, we
compare nonperturbative QCD predictions for the asymptotic behavior of DIS
structure functions and parton distribution functions (PDFs) to the $x$ and $Q$
dependence of phenomenological PDFs. In the CT18 NNLO global QCD analysis,
higher-order radiative contributions and functional mimicry of PDF
parametrizations result in about one unit of uncertainty in the effective
powers of $(1-x)$ falloff of nucleon PDFs. Similar uncertainties are present in
the case of the pion PDF, an object of growing interest in phenomenology.
