  We apply a classical mathematical problem, the moment problem, with its
related mathematical achievements, to the study of the parton distribution
function (PDF) in hadron physics, and propose a strategy to sieve the moments
of the PDF by exploiting its properties such as continuity, unimodality, and
symmetry. Through an error-inclusive sifting process, we refine three sets of
PDF moments from Lattice QCD. This refinement significantly reduces the errors,
particularly for higher order moments, and locates the peak of PDF
simultaneously. As our strategy is universally applicable to PDF moments from
any method, we strongly advocate its integration into all PDF moment
calculations.
