  A new parametrization for the parton distribution functions with a higher
flexibility in the small-$x$ region is presented. It has been implemented in
the xFitter open-source PDF fitting tool, and compared to the default xFitter
parametrization, used for the determination of the HERAPDF set. It has been
found that the combined inclusive HERA I+II data can be described using NNLO
theory with a significantly higher quality than HERAPDF2.0: the $\chi^2$ is
reduced by more than 60 units, having used only four more parameters. Our
result highlights a significant parametrization bias in the default xFitter
parametrization at small $x$, which would lead to even more dramatic effects
when used for higher energy colliders, where the small-$x$ region is more
relevant. We also find that the inclusion of small-$x$ resummation leads to a
further reduction by approximately 30 extra units in $\chi^2$. In this
contribution, we review the results of the recent paper "A new simple PDF
parametrization: improved description of the HERA data" (arXiv:1902.11125).
