Bendel R B, Higgins S S, Teberg J E, Pyke D A
Program in Statistics, Washington State University, 99164, Pullman, WA, USA.
Oecologia. 1989 Mar;78(3):394-400. doi: 10.1007/BF00379115.
The moment skewness coefficient, coefficient of variation and Gini coefficient are contrasted as statistical measures of inequality among members of plant populations. Constructed examples, real data examples, and distributional considerations are used to illustrate pertinent properties of these statistics to assess inequality. All three statistics possess some undesirable properties but these properties are shown to be often unimportant with real data. If the underlying distribution of the variable follows the often assumed two-parameter lognormal model, it is shown that all three statistics are likely to be highly and positively correlated. In contrast, for distributions which are not two-parameter lognormally distributed, and when the distribution is not concentrated near zero, the coefficient of variation and Gini coefficient, which are sensitive to small shifts in the mean, are often of little practical use in ordering the equality of populations. The coefficent of variation is more sensitive to individuals in the right-hand tail of a distribution than is the Gini coefficient. Therefore, the coefficient of variation may often be recommended over the Gini coefficient if a measure of relative precision is selected to assess inequality. The skewness coeficient is suggested when the distribution is either three-parameter lognormally distributed (or close to such), or when a measure of relative precision is not indicated.
将矩偏度系数、变异系数和基尼系数作为植物种群成员间不平等的统计量进行对比。通过构建示例、实际数据示例以及分布考量来阐述这些统计量评估不平等的相关特性。这三个统计量都具有一些不理想的特性，但在实际数据中这些特性往往并不重要。如果变量的基础分布遵循通常假定的双参数对数正态模型，那么可以表明这三个统计量很可能高度正相关。相反，对于非双参数对数正态分布且分布不集中在零附近的情况，对均值的小偏移敏感的变异系数和基尼系数，在对种群平等性进行排序时通常没什么实际用途。变异系数比基尼系数对分布右尾的个体更敏感。因此，如果选择一个相对精度的度量来评估不平等，那么变异系数可能常常比基尼系数更值得推荐。当分布为三参数对数正态分布（或接近此分布），或者未指明相对精度的度量时，建议使用偏度系数。
