  A percentile-based bibliometric indicator is an indicator that values
publications based on their position within the citation distribution of their
field. The most straightforward percentile-based indicator is the proportion of
frequently cited publications, for instance the proportion of publications that
belong to the top 10% most frequently cited of their field. Recently, more
complex percentile-based indicators were proposed. A difficulty in the
calculation of percentile-based indicators is caused by the discrete nature of
citation distributions combined with the presence of many publications with the
same number of citations. We introduce an approach to calculating
percentile-based indicators that deals with this difficulty in a more
satisfactory way than earlier approaches suggested in the literature. We show
in a formal mathematical framework that our approach leads to indicators that
do not suffer from biases in favor of or against particular fields of science.
