Arachchige Chandima N P G, Prendergast Luke A, Staudte Robert G
Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia.
J Appl Stat. 2020 Aug 20;49(2):268-290. doi: 10.1080/02664763.2020.1808599. eCollection 2022.
The coefficient of variation is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect it. Additionally, for skewed distributions the mean and standard deviation may be difficult to interpret and, consequently, that may also be the case for the . Here we investigate the extent to which quantile-based measures of relative dispersion can provide appropriate summary information as an alternative to the CV. In particular, we investigate two measures, the first being the interquartile range (in lieu of the standard deviation), divided by the median (in lieu of the mean), and the second being the median absolute deviation, divided by the median, as robust estimators of relative dispersion. In addition to comparing the influence functions of the competing estimators and their asymptotic biases and variances, we compare interval estimators using simulation studies to assess coverage.
变异系数通常用于衡量相对离散程度。然而，由于它基于样本均值和标准差，异常值可能会对其产生不利影响。此外，对于偏态分布，均值和标准差可能难以解释，因此变异系数也可能如此。在这里，我们研究基于分位数的相对离散程度度量在多大程度上可以作为变异系数的替代方法，提供适当的汇总信息。特别是，我们研究了两种度量方法，第一种是四分位距（代替标准差）除以中位数（代替均值），第二种是中位数绝对偏差除以中位数，作为相对离散程度的稳健估计量。除了比较竞争估计量的影响函数及其渐近偏差和方差外，我们还通过模拟研究比较区间估计量以评估覆盖率。
