  Sets of parton distribution functions (PDFs) of the proton are reported for
the leading (LO), next-to-leading (NLO) and next-to-next-to leading order
(NNLO) QCD calculations. The parton distribution functions are determined with
the HERAFitter program using the data from the HERA experiments and preserving
correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets
are used to study cross-section ratios and their uncertainties when calculated
at different orders in QCD. A reduction of the overall theoretical uncertainty
is observed if correlations between the PDF sets are taken into account for the
ratio of $WW$ di-boson to $Z$ boson production cross sections at the LHC.
