  There are a number of mathematical formalisms of the term "outlier" in
statistics, though there is no consensus on what the right notion ought to be.
Accordingly, we try to give a consistent and robust definition for a specific
type of outliers defined via order statistics. Our approach is based on ratios
of partial sums of order statistics to investigate the tail behaviors of
hypothetical and empirical distributions. We simulate our statistic on a set of
distributions to mark potential outliers and use an algorithm to automatically
select a cut-off point without the need of any further a priori assumption.
Finally, we show the efficacy of our statistic by a simulation study on
distinguishing two Pareto tails outside of the L\'{e}vy stable region.
