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There are a number of mathematical formalisms of the term "outlier" instatistics, 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 specifictype of outliers defined via order statistics. Our approach is based on ratiosof partial sums of order statistics to investigate the tail behaviors ofhypothetical and empirical distributions. We simulate our statistic on a set ofdistributions to mark potential outliers and use an algorithm to automaticallyselect 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 ondistinguishing two Pareto tails outside of the L\'{e}vy stable region.

On a Notion of Outliers Based on Ratios of Order Statistics