  It is now widely recognized that large Bjorken $x$ data play an important
role in global analyses of Parton Distribution Functions (PDFs) even at
collider energies, through perturbative QCD evolution. For values of the scale
of the reaction, $Q^2$, in the multi-GeV region the structure functions at
large $x$ present resonance structure. Notwithstanding, these data can be
incorporated in the analyses by using quark-hadron duality or approximate
scaling of the structure function data averaged over their resonance structure.
Several averaging methods have been proposed using either the PDFs Mellin
moments, or their truncated moments. We propose an alternative method using
Bernstein polynomials integrals, or Bernstein moments. Bernstein moments render
a smooth form of the structure function in the resonance region. Furthermore,
being based on a different averaging criterion than the methods adopted so far,
they provide a new framework for understanding the possible mechanisms giving
origin to the phenomenon of quark-hadron duality.
