Uncertainties on parton distribution functions from the ZEUS NLO QCD fit to data on deep inelastic scattering

An NLO QCD analysis of the ZEUS data on $e^+ p$ deep inelastic scattering together with fixed-target data has been performed from which the gluon and quark densities of the proton and the value of the strong coupling parameter, $\alpha_s(M_Z^2)$, have been extracted. The study includes a full treatment of the experimental systematic uncertainties, including point-to-point correlations. Different ways of incorporating correlated systematic uncertainties into the fit are discussed and compared.