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The effect of dragon-kings on the estimation of scaling law parameters

Cabrera-Arnau, C; Bishop, SR; (2020) The effect of dragon-kings on the estimation of scaling law parameters. Scientific Reports , 10 , Article 20226. 10.1038/s41598-020-77232-6. Green open access

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Abstract

Scaling laws are used to model how diferent quantifable properties of cities, such as the number of road trafc accidents or average house prices, vary as a function of city population size, with parameters estimated from data. Arcaute et al. raised the issue of whether specifc cities with extremely large population sizes, known as dragon-kings, should be considered separately from other smaller cities when estimating the scaling law parameters since the two types of cities tend to display diferent behaviour. Through the analysis of randomly generated samples, we fnd that the inclusion of dragon-kings in the scaling analysis does not afect the estimated values for the parameters but only provided that all the data points satisfy the same scaling law. We also analyse randomly generated samples where data corresponding to a particular city deviates from the scaling law followed by the rest of the cities. We then show that deviations corresponding to dragon-king cities have the most signifcant efect on the estimated values of the scaling parameters. The extent of this efect also depends on which estimation procedure is used. Our results have important implications on the suitability of scaling laws as a model for urban systems.

Type: Article
Title: The effect of dragon-kings on the estimation of scaling law parameters
Open access status: An open access version is available from UCL Discovery
DOI: 10.1038/s41598-020-77232-6
Publisher version: https://doi.org/10.1038/s41598-020-77232-6
Language: English
Additional information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10118432
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