The Four Basic Properties Of Rank†Size Hierarchical Distributions: Their Characteristics And Interrelationships

In sets of empirical data that can he described by a skewed distribution function such as the rank size, relationships exist among the total observations, the relative size of the largest observation, the number of categories, and the slope of the distribution We consider only one phenomenon, the distribution of urban population into urban centers of various sizes. The properties become the total urban population, the size of the largest center, the number of places, and the slope characterizing the distribution. We present an analytical model which defines these relationships for various sizes of urban populations and various slopes. Numerical examples demonstrate the results of the analysis. The advantages of using the Principal Axis to measure slope are discussed, and we demonstrate this method. The model shows clearly how the proportion of the urban population in the largest center declines and also how the number of smaller centers grows dramatically as total urban population increases. Implications are discussed for the nature of changes to be expected in those areas of the world where urbanization is still taking place, such as Asia, Latin America, and Africa.