世界上所有自然城市的齐普夫定律
Zipf's Law for All the Natural Cities around the World
摘要：
围绕齐普夫定律关于城市规模的研究的两个基本问题是，这个定律是否成立以及为什么成立。本文不涉及后者的问题，为什么，而是调查是否齐普夫定律在全球范围内成立，从而涉及世界各地的所有城市。与以往的研究不同，这些研究主要依赖于人口等传统的人口普查数据，以及人口普查局对城市的定义，我们采用自然（数据本身说明）划定的城市，或自然城市，更准确地说，为了检验齐普夫定律。我们发现，齐普夫定律在全球范围内对所有自然城市都非常适用，并且在大陆层面上几乎仍然有效，除了非洲在某些时刻。我们进一步研究了国家一级的法律，并注意到Zipf的法律在不同国家或不同时间被违反。这种违反主要是由于我们的局限性;我们仅限于个别国家，或对城市规模分布的静态看法。本文的中心论点是齐普夫定律是普适的，因此我们必须使用正确的范围才能遵守它。第一大国的城市数量是第二大国的两倍，是第三大国的三倍，等等。这些发现对大数据和城市科学有着深远的影响。关键词：夜间影像，城市规模分布，首尾划分规则，首尾间断，大数据
英文摘要：
Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a global setting, thus involving all cities around the world. Unlike previous studies, which have mainly relied on conventional census data such as populations, and census-bureau-imposed definitions of cities, we adopt naturally (in terms of data speaks for itself) delineated cities, or natural cities, to be more precise, in order to examine Zipf's law. We find that Zipf's law holds remarkably well for all natural cities at the global level, and remains almost valid at the continental level except for Africa at certain time instants. We further examine the law at the country level, and note that Zipf's law is violated from country to country or from time to time. This violation is mainly due to our limitations; we are limited to individual countries, or to a static view on city-size distributions. The central argument of this paper is that Zipf's law is universal, and we therefore must use the correct scope in order to observe it. We further find Zipf's law applied to city numbers; the number of cities in the first largest country is twice as many as that in the second largest country, three times as many as that in the third largest country, and so on. These findings have profound implications for big data and the science of cities. Keywords: Night-time imagery, city-size distributions, head/tail division rule, head/tail breaks, big data
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