空间和规模分布差异的组间不均衡指数

构造组间相对不均衡指数, 用来描述一个地理系统相对于另一个地理系统发展的不平衡关系, 或一个系统内部的一个指标相对于另一个指标的不均衡关系。首先改变常规组内不均衡指数(即基于Lorenz曲线的Gini系数)的数学表达式, 然后利用新的表达式, 将组内不均衡指数推广到组间不均衡指数表达式。在应用过程中, 两种不均衡指数可以集成到同一个逻辑框架。以京津冀、长江三角洲和珠江三角洲的城市体系为实证对象, 借助新的公式计算组内和组间不均衡指数, 揭示城市系统的时空演化特征。

Inequality Indexes for Measuring Between-Groups Mean Difference of Size and Spatial Distributions

A set of new inequality indexes are constructed to measure the relative unbalanced difference between regions or groups of elements in a geographical systems. Firstly, the within-group inequality index, namely, the Gini coefficient based on the Lorenz curve, is transformed into a new mathematical expression. Then, based on the new formula, the within-group index is generalized to between-group inequality index. Technically, the two types of inequality indexes can be integrated into the same logic framework. As an example, the new formulae are applied to three systems of cities in China, including Beijing-Tianjin-Hebei region, Yangtze River Delta, and Pearl River Delta. The results display a spatio-temporal evolution patterns of relative mean differences within and between these urban systems.