How sensitive is city size distribution to the definition of city? The case of Spain

Puente‐Ajovín, Miguel; Ramos, Arturo; Sanz‐Gracia, Fernando; Arribas‐Bel, Daniel

doi:10.1016/j.econlet.2020.109643

Cited by 9 publications

(7 citation statements)

References 19 publications

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“…On the contrary, we find a great variability, depending on the years considered, regarding the best density. This outcome is in line with the key message derived from [38,39]. This reflects the effort made by most countries in the reduction of CO 2 emissions, with some countries with a higher effort than others, leading to year-to-year shifts in the statistical distribution of CO 2 emissions among nations.…”

Section: Introductionsupporting

confidence: 82%

“…where erf denotes the error function associated to the standard normal distribution. The 2-mixture of normal distributions (2N), is [20,21,22,28,38,39,7]…”

Section: The Distributionsmentioning

confidence: 99%

“…In this paper we perform the first attempt, to the best of our knowledge, to define the densities that fit best to the observed data. The distributions chosen are the exponentiated versions of that in [2], that is to say, the normal (N), the asymmetric double Laplace normal (adLN) (exponentiated version of the double Pareto lognormal, dPLN), the exponential tails normal (ETN) (exponentiated version of the Pareto tails lognormal, PTLN) 2 and the exponentiated version of two densities recently introduced in the literature of city sizes and strike size [28,6,22,21,48,38,39,7], namely a mixture of two (2N) or three (3N) normal distributions (see also, e.g., [35]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Log-growth rates of CO2: An empirical analysis

Peña

Puente‐Ajovín

Ramos

et al. 2022

Physica A: Statistical Mechanics and its Applications

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Section: Introductionsupporting

confidence: 82%

“…where erf denotes the error function associated to the standard normal distribution. The 2-mixture of normal distributions (2N), is [20,21,22,28,38,39,7]…”

Section: The Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Log-growth rates of CO2: An empirical analysis

Peña

Puente‐Ajovín

Ramos

et al. 2022

Physica A: Statistical Mechanics and its Applications

Self Cite

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“…In a similar vein, analyses of city size distribution are sensitive to the definition of cities or “UCs,” which obviously aligns with observations made in urban polycentricity research (e.g., Zhang and Derudder 2019) and the wider field of urban science (e.g., Puente‐Aljovín et al 2020). Moreover, there is substantial ambiguity about what density threshold best captures global urban population distributions and whether a single threshold as provided by the GHS‐UCDB (Florczyk et al 2019) is best practice (Borel‐Saladin 2016; Angel et al 2019; Onda et al 2019; Denis 2020; Statham et al 2020).…”

Section: Summary and Discussionsupporting

confidence: 68%

Mapping the Spatial Conditions of Polycentric Urban Development in Europe: An Open‐source Software Tool

Caset

Derudder

Migerode

et al. 2021

Geographical Analysis

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Urban polycentricity has become a key concept in urban and regional studies and is increasingly adopted as an organizational framework for conducting empirical research. Within this literature, polycentric urban regions are commonly defined as territories that have multiple, proximately located (sub)centers and are characterized by balanced urban development. However, analytical‐operational frameworks to identify and classify PURs are often ad hoc efforts to answer a specific research question and underlying work is often shelved rather than shared and/or made accessible. As a result, challenges associated with generalizability, reproducibility, and replicability clearly loom large in the urban polycentricity literature. Against this backdrop, this article describes the discrepancy between a rich debate on polycentricity and the paucity of tools enabling the disambiguation and reproducibility of results claimed by various authors around this polysemic concept. We present an online and open tool—PURban—that brings together the major analytical‐operational frameworks and data sets in urban polycentricity research and allows parametrizing key operational choices. To illustrate the tool, we demonstrate how it facilitates the identification, mapping and analysis of degrees of morphological polycentricity in European urban systems. We conclude by reflecting on how this tool can act as a catalyst for future research on urban polycentricity.

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“…We will also consider 2-mixtures and 3-mixtures ( McLachlan & Peel, 2003 ) of log-normal distributions, like in Kwong and Nadarajah (2019) ; Bǎncescu et al (2019) ; Su (2020) ; Puente-Ajovín et al (2020a , b) ; Campolieti and Ramos (2021) :

where 0 ≤ p 1 , 1 − p 1 ≤ 1, and

where 0 ≤ p 1 , p 2 , 1 − p 1 − p 2 ≤ 1.…”

Section: Methodsmentioning

confidence: 99%