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The concentration of a distribution toward a lower bound is a conceptuallysimple property that lacks a global descriptive statistic. We term thisproperty shift and define it as the distance of a central tendency from anupper bound, expressed as a proportion of a finite range. We derive ageneralizable low complexity measure of shift, $\mathcal{S}$, and demonstrateits properties, its use with theoretical distributions, and its relation toskewness. We then use $\mathcal{S}$ as the basis for a uniquely directionalmeasure of distance, $\Delta\mathcal{S}$. We prove |$\Delta\mathcal{S}$| as aformal distance metric and demonstrate its close relation to metrics of highercomplexity. The close relationship between |$\Delta\mathcal{S}$| andWasserstein Distance (slope = 1.03, $r^{2}$ = 0.99) provoked a preliminaryanalysis of computing time. The computation of |$\Delta\mathcal{S}$| wasconsistently faster than an efficient 1-dimensional Wasserstein Distance,whereby the difference in compute time grew with sample size. We demonstrate$\mathcal{S}$ as a measure of species rarity having greater validity thanmeasures based on skewness and abundance thresholds. We then demonstrate$\mathcal{S}$ as a measure of poverty that closely relates to establishedpoverty indices, but without reliance on poverty lines. Finally we demonstratethe use of $\mathcal{S}$, $\Delta\mathcal{S}$, and |$\Delta\mathcal{S}$| in ananalysis of image data, revealing a signal of detection for discrete events andgradual color shifts that was indiscernible from that produced by WassersteinDistance. As a simple and general property, $\mathcal{S}$ and its relatedmeasures have a high degree of potential application across fields.

Novel shift statistics with applications to ecology, economics, and image analysis