  We explore the role of parametrizations for nonperturbative QCD functions in
global analyses, with a specific application to extending a phenomenological
analysis of the parton distribution functions (PDFs) in the charged pion
realized in the xFitter fitting framework. The parametrization dependence of
PDFs in our pion fits substantially enlarges the uncertainties from the
experimental sources estimated in the previous analyses. We systematically
explore the parametrization dependence by employing a novel technique to
automate generation of polynomial parametrizations for PDFs that makes use of
B\'ezier curves. This technique is implemented in a C++ module Fant\^omas that
is included in the xFitter program. Our analysis reveals that the sea and gluon
distributions in the pion are not well disentangled, even when considering
measurements in leading-neutron deep inelastic scattering. For example, the
pion PDF solutions with a vanishing gluon and large quark sea are still
experimentally allowed, which elevates the importance of ongoing lattice and
nonperturbative QCD calculations, together with the planned pion scattering
experiments, for conclusive studies of the pion structure.
