The concept of shift is often invoked to describe directional differences in statistical moments but has not yet been established as a property of individual distributions. In the present study, we define distributional shift (DS) as the concentration of frequencies towards the lowest discrete class and derive its measurement from the sum of cumulative frequencies. We use empirical datasets to demonstrate DS as an advantageous measure of ecological rarity and as a generalisable measure of poverty and scarcity. We then define relative distributional shift (RDS) as the difference in DS between distributions, yielding a uniquely signed (i.e., directional) measure. Using simulated random sampling, we show that RDS is closely related to measures of distance, divergence, intersection, and probabilistic scoring. We apply RDS to image analysis by demonstrating its performance in the detection of light events, changes in complex patterns, patterns within visual noise, and colour shifts. Altogether, DS is an intuitive statistical property that underpins a uniquely useful comparative measure.

翻译：“偏移”这一概念常被用于描述统计矩的方向性差异，但尚未被确立为个体分布的一种属性。本研究将分布偏移（DS）定义为频数向最低离散类别的集中程度，并基于累积频数之和推导出其度量方法。我们利用实证数据集证明，DS既是生态稀有性的一种优势度量指标，也是贫困与稀缺性的一种可泛化度量指标。进一步地，我们将相对分布偏移（RDS）定义为分布间DS的差值，从而得到一种具有唯一符号（即方向性）的度量。通过模拟随机抽样，我们证明RDS与距离、散度、交集及概率评分等度量密切相关。我们将RDS应用于图像分析，展示了其在光事件检测、复杂模式变化识别、视觉噪声中模式检测以及颜色偏移检测中的性能。综上，DS是一种直观的统计属性，为一种具有独特实用性的比较度量奠定了基础。