Quantifying Proportional Variability
Quantifying Proportional Variability
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DOI：
10.1371/journal.pone.0084074
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发表时间：
2013-12-30
期刊：
影响因子：
3.7
通讯作者：
Borowski, Peter
中科院分区：
文献类型：
--
作者：
Heath, Joel P.;Borowski, Peter
真实的量可以经历如此广泛的动态变化，以至于平均值通常是测量可变性的无意义参考点。尽管它们被广泛应用，但像变异系数这样的技术并不是真正成比例的，并且表现出病理学性质。非参数测量比例变异性（PV）[1]解决了这些问题，并提供了一种强大的方法来总结和比较表现出不同动态行为的数量变化。变异不是基于与平均值的偏差，而是简单地通过相互比较数字来量化，不需要对集中趋势或潜在的统计分布进行假设。虽然PV已经介绍了之前，并已被应用在各种情况下，人口动态，在这里，我们提出了一个更深入的分析，这个新的措施，推导出解析表达式的PV的几个一般分布，并提出新的比较与变异系数，展示的情况下，PV是更有利的措施。我们表明，PV提供了一种易于解释的方法来测量和比较变化，可以普遍应用于整个科学，从股票市场的稳定性，气候变化的背景。
Real quantities can undergo such a wide variety of dynamics that the mean is often a meaningless reference point for measuring variability. Despite their widespread application, techniques like the Coefficient of Variation are not truly proportional and exhibit pathological properties. The non-parametric measure Proportional Variability (PV) [1] resolves these issues and provides a robust way to summarize and compare variation in quantities exhibiting diverse dynamical behaviour. Instead of being based on deviation from an average value, variation is simply quantified by comparing the numbers to each other, requiring no assumptions about central tendency or underlying statistical distributions. While PV has been introduced before and has already been applied in various contexts to population dynamics, here we present a deeper analysis of this new measure, derive analytical expressions for the PV of several general distributions and present new comparisons with the Coefficient of Variation, demonstrating cases in which PV is the more favorable measure. We show that PV provides an easily interpretable approach for measuring and comparing variation that can be generally applied throughout the sciences, from contexts ranging from stock market stability to climate variation.