The Spanish spatial city size distribution

González‐Val, Rafael

doi:10.1177/2399808320941860

Cited by 6 publications

(5 citation statements)

References 45 publications

(85 reference statements)

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“…Frontiers in Built Environment frontiersin.org represented by the Pareto distribution (Jiang and Jia, 2011;Chen, 2016;González-Val, 2020), whereas in India, China, and Japan, the distribution shows a transition from a lognormal distribution in the early periods to Pareto in later periods (Kuninaka and Matsushita, 2008;Luckstead and Devadoss, 2014;Li and Zhang, 2018). In recent years, research has been more in-depth; researchers have discussed the urban size from a mixture of a lognormal distribution and Pareto distribution (Luckstead et al, 2017;Băncescu et al, 2019).…”

Section: Hypothesis Of the Double Pareto Lognormal Distributionmentioning

confidence: 99%

Scaling the living space: Zipf’s law for traditional courtyard houses in South China

Zhou

2022

Front. Built Environ.

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In the traditional feudalistic society of China, there is a characteristic residential pattern of several core families with common ancestors living together in one house, as far as possible. Hence, the habitation of large families and their social dynamic always have a complex function and hierarchical structure. In this article, we consider a courtyard in South China as an example to enable a discussion of the mathematical relationship among the five basic functional spaces in it. Based on Zipf’s law, we find that the distribution of the five types of spaces, from large to small, can be described by the Pareto distribution with a shape parameter close to −1. Moreover, the Zipf parameters of different houses in the same area conform to the double Pareto distribution. This suggests that the size and shape of a residence also follows well-defined scaling laws. Additionally, it indicates that houses, at least traditional Chinese houses, have strong self-organization and self-similarity. It also shows that the power law of the Pareto distribution is applicable not only to the macro scale of the city but also the micro scale of housing.

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Section: Hypothesis Of the Double Pareto Lognormal Distributionmentioning

confidence: 99%

Scaling the living space: Zipf’s law for traditional courtyard houses in South China

Zhou

2022

Front. Built Environ.

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“…Previous researches have shown that trajectories in human society exhibit the statistically similar Lévy ight characteristics, such as the traces of bank note [12], human mobility [13], and COVID-19 con rmed cases [14]. Many studies have shown that the rank-order of cities in the United States [15], India [16], and Spain [17] shows Lévy ights characteristics, following Pareto law [15,18] or Zipf's law [19,20]. Researchers have also employed power-law adjusted metropolitan indicators [21] to assess urban land use efficiency in Chinese cities.…”

Section: Introductionmentioning

confidence: 97%

“…is paper covers the most commonly used data types for measuring urban development [17]. Firstly, it is clear that the research object is the steplengths of urban development trajectory [25], with economical development as horizontal axis and social development as vertical axis.…”

Section: Introductionmentioning

confidence: 99%

The Lévy Flight of Cities: Analyzing Social‐Economical Trajectories with Auto‐Embedding

Tian

Zhao

Yin

et al. 2022

Discrete Dynamics in Nature and Society

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Lévy flights are useful in stochastic measurement, such as biology, human mobility, and financial mathematics, where trajectories contain many short flights and some long flights, and the step-lengths follow a power-law distribution. For cities inhabited by human beings, this paper proposes to use latent factors to study social-economical development trajectories and observes that the trajectories of four Asian cities exhibit Lévy flight characteristics. We collect the social and economical data such as GDP, goods producing industries, population, and general tertiary education, and map these data into social or economical factor through a deep-learning embedding method auto-encoder. We find that the step-lengths of these urban social-economical trajectories can be fitted approximately as a power-law distribution. We use the stochastic multiplicative processes (SMPs) to explain such pattern, wherein the presence of a boundary constraint, the SMP, leads to a power-law distribution. It means that these urban social-economical trajectories follow a Lévy flight pattern, where some years have large changes and many years have little changes.

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“…Understanding the intimate pattern of population distribution and accounting for the intrinsic socioeconomic dynamics of urban-rural hierarchies, are key arguments of applied economics, regional science, spatial planning, and political geography [1][2][3]. By considering population, settlements, and activities, both separately and together, comparative analyses of urban-rural hierarchies that use population (or economic) data at different aggregation levels were rather infrequent in both advanced economies and emerging countries [4][5][6]. The need for coherent, high-quality statistics limits the practical applicability of theoretical Land 2024, 13, 415 2 of 15 exercises referring to the rank-size relationship and, more specifically, to the empirical verification of Zipf's law for specific variables, basically population or, less frequently, settlements and activities [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Envisaging the Intrinsic Departure from Zipf’s Law as an Indicator of Economic Concentration along Urban–Rural Gradients

Sateriano,

Quaranta,

Salvia

et al. 2024

Land

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A rank-size rule following Zipf’s law was tested along a complete urban–rural hierarchy in Greece using 2021 census data released at different administrative levels. Testing five econometric specifications (linear, quadratic, and cubic forms, together with refined logistic and Gompertz forms) on log-transformed population numbers, deviations from the rank-size rule were assumed as an indicator of economic concentration (considering settlements, population, and activities jointly) along the density gradient in Greece. This hypothesis was verified using progressively disaggregated population numbers at (i) regional units (n = 75), (ii) ‘Kallikratis’ municipalities (n = 333), (iii) ‘Kapodistrian’ municipalities (n = 1037), and (iv) local communities (n = 6126). Econometric results were stable across geographical levels and indicate a relatively poor fit of linear specifications, the classical formulation of Zipf’s law. Quadratic specifications displayed a good fit for all territorial levels outperforming cubic specifications. Gompertz specifications outperformed logistic specifications under aggregate partitions (e.g., regional units and ‘Kallikratis’ municipalities). Quadratic specifications outperformed both logistic and Gompertz specifications under disaggregated levels of investigation (‘Kapodistrian’ municipalities and local communities). Altogether, these findings indicate the persistence of non-linear rank-size relationships estimated over a cross-section of population data at progressively detailed observational units. Such evidence enriches the recent literature on Zipf’s law, demonstrating the inherent complexity of rank-size rules tested on real data along the whole density gradient in a given country.

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The Spanish spatial city size distribution

Cited by 6 publications

References 45 publications

Scaling the living space: Zipf’s law for traditional courtyard houses in South China

Scaling the living space: Zipf’s law for traditional courtyard houses in South China

The Lévy Flight of Cities: Analyzing Social‐Economical Trajectories with Auto‐Embedding

Envisaging the Intrinsic Departure from Zipf’s Law as an Indicator of Economic Concentration along Urban–Rural Gradients

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