The statistics of urban scaling and their connection to Zipf's law.

Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed...

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Autores principales:	Andres Gomez-Lievano, Hyejin Youn, Luís M A Bettencourt
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2012
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b24ae0a17f0349189f31e1287683059a
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spelling	oai:doaj.org-article:b24ae0a17f0349189f31e1287683059a2021-11-18T07:12:05ZThe statistics of urban scaling and their connection to Zipf's law.1932-620310.1371/journal.pone.0040393https://doaj.org/article/b24ae0a17f0349189f31e1287683059a2012-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/22815745/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed in detail, raising important questions about the full characterization of urban properties and how scaling relations may emerge in these larger contexts. Here, we build a self-consistent statistical framework that characterizes the joint probability distributions of urban indicators and city population sizes across an urban system. To develop this framework empirically we use one of the most granular and stochastic urban indicators available, specifically measuring homicides in cities of Brazil, Colombia and Mexico, three nations with high and fast changing rates of violent crime. We use these data to derive the conditional probability of the number of homicides per year given the population size of a city. To do this we use Bayes' rule together with the estimated conditional probability of city size given their number of homicides and the distribution of total homicides. We then show that scaling laws emerge as expectation values of these conditional statistics. Knowledge of these distributions implies, in turn, a relationship between scaling and population size distribution exponents that can be used to predict Zipf's exponent from urban indicator statistics. Our results also suggest how a general statistical theory of urban indicators may be constructed from the stochastic dynamics of social interaction processes in cities.Andres Gomez-LievanoHyejin YounLuís M A BettencourtPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 7, Iss 7, p e40393 (2012)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Andres Gomez-Lievano Hyejin Youn Luís M A Bettencourt The statistics of urban scaling and their connection to Zipf's law.
description	Urban scaling relations characterizing how diverse properties of cities vary on average with their population size have recently been shown to be a general quantitative property of many urban systems around the world. However, in previous studies the statistics of urban indicators were not analyzed in detail, raising important questions about the full characterization of urban properties and how scaling relations may emerge in these larger contexts. Here, we build a self-consistent statistical framework that characterizes the joint probability distributions of urban indicators and city population sizes across an urban system. To develop this framework empirically we use one of the most granular and stochastic urban indicators available, specifically measuring homicides in cities of Brazil, Colombia and Mexico, three nations with high and fast changing rates of violent crime. We use these data to derive the conditional probability of the number of homicides per year given the population size of a city. To do this we use Bayes' rule together with the estimated conditional probability of city size given their number of homicides and the distribution of total homicides. We then show that scaling laws emerge as expectation values of these conditional statistics. Knowledge of these distributions implies, in turn, a relationship between scaling and population size distribution exponents that can be used to predict Zipf's exponent from urban indicator statistics. Our results also suggest how a general statistical theory of urban indicators may be constructed from the stochastic dynamics of social interaction processes in cities.
format	article
author	Andres Gomez-Lievano Hyejin Youn Luís M A Bettencourt
author_facet	Andres Gomez-Lievano Hyejin Youn Luís M A Bettencourt
author_sort	Andres Gomez-Lievano
title	The statistics of urban scaling and their connection to Zipf's law.
title_short	The statistics of urban scaling and their connection to Zipf's law.
title_full	The statistics of urban scaling and their connection to Zipf's law.
title_fullStr	The statistics of urban scaling and their connection to Zipf's law.
title_full_unstemmed	The statistics of urban scaling and their connection to Zipf's law.
title_sort	statistics of urban scaling and their connection to zipf's law.
publisher	Public Library of Science (PLoS)
publishDate	2012
url	https://doaj.org/article/b24ae0a17f0349189f31e1287683059a
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The statistics of urban scaling and their connection to Zipf's law.

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