英文标题：
《Cross Ranking of Cities and Regions: Population vs. Income》
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作者：
Roy Cerqueti and Marcel Ausloos
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最新提交年份：
2015
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英文摘要：
  This paper explores the relationship between the inner economical structure of communities and their population distribution through a rank-rank analysis of official data, along statistical physics ideas within two techniques. The data is taken on Italian cities. The analysis is performed both at a global (national) and at a more local (regional) level in order to distinguish \"macro\" and \"micro\" aspects. First, the rank-size rule is found not to be a standard power law, as in many other studies, but a doubly decreasing power law. Next, the Kendall and the Spearman rank correlation coefficients which measure pair concordance and the correlation between fluctuations in two rankings, respectively, - as a correlation function does in thermodynamics, are calculated for finding rank correlation (if any) between demography and wealth. Results show non only global disparities for the whole (country) set, but also (regional) disparities, when comparing the number of cities in regions, the number of inhabitants in cities and that in regions, as well as when comparing the aggregated tax income of the cities and that of regions. Different outliers are pointed out and justified. Interestingly, two classes of cities in the country and two classes of regions in the country are found. \"Common sense\" social, political, and economic considerations sustain the findings. More importantly, the methods show that they allow to distinguish communities, very clearly, when specific criteria are numerically sound. A specific modeling for the findings is presented, i.e. for the doubly decreasing power law and the two phase system, based on statistics theory, e.g., urn filling. The model ideas can be expected to hold when similar rank relationship features are observed in fields. It is emphasized that the analysis makes more sense than one through a Pearson value-value correlation analysis.
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中文摘要：
本文通过对官方数据的秩次分析，结合两种技术中的统计物理思想，探讨了社区内部经济结构与人口分布之间的关系。数据来自意大利城市。为了区分“宏观”和“微观”方面，分析在全球（国家）和更地方（区域）层面上进行。首先，研究发现，排名大小规则并不像许多其他研究那样是一个标准的幂律，而是一个双倍递减的幂律。接下来，计算Kendall和Spearman秩相关系数，分别测量配对一致性和两个排名波动之间的相关性，就像热力学中的相关函数一样，以发现人口统计学和财富之间的秩相关（如果有）。结果显示，在比较各地区的城市数量、城市和地区的居民数量，以及比较各城市和地区的总税收收入时，不仅整个（国家）数据集存在全球差异，而且还存在（地区）差异。指出并证明了不同的异常值。有趣的是，我们发现了该国的两类城市和两类地区。“常识”的社会、政治和经济考虑支持了这一发现。更重要的是，这些方法表明，当具体标准在数字上合理时，它们可以非常清楚地区分社区。基于统计理论（如urn填充），对研究结果进行了具体建模，即双递减幂律和两相系统。当在现场观察到类似的秩关系特征时，模型思想有望成立。需要强调的是，这种分析比通过皮尔逊价值相关分析更有意义。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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