The Negative Exponential Density Gradient and the Standard Radius: Mathematical and Empirical Relationships
研究了城市人口分布的负指数密度梯度模型与中心测量指标之间的数学关系，并用多城市数据验证了该关系。
This paper demonstrates for urban areas a direct relationship between the summary measures of centrography and the slope parameter of the negative exponential density gradient model. Starting with some basic assumptions about the form of urban population distributions, a mathematical relationship between the methods is derived by applying the centrographic technique to an exponentially distributed urban population. By use of data from a diverse sample of cities that vary in population, region, area, and time of data collection, the relationship is tested empirically. The results of the empirical analysis are compared with the predictions of the derived relationship, and the causes of differences between them are discussed.