IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v409y2014icp175-182.html
   My bibliography  Save this article

Empirical analysis on the connection between power-law distributions and allometries for urban indicators

Author

Listed:
  • Alves, L.G.A.
  • Ribeiro, H.V.
  • Lenzi, E.K.
  • Mendes, R.S.

Abstract

We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.

Suggested Citation

  • Alves, L.G.A. & Ribeiro, H.V. & Lenzi, E.K. & Mendes, R.S., 2014. "Empirical analysis on the connection between power-law distributions and allometries for urban indicators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 175-182.
  • Handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:175-182
    DOI: 10.1016/j.physa.2014.04.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114003641
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2014.04.046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luiz G A Alves & Haroldo V Ribeiro & Ervin K Lenzi & Renio S Mendes, 2013. "Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    2. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    3. Luís M A Bettencourt & José Lobo & Deborah Strumsky & Geoffrey B West, 2010. "Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    4. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    5. Luis Bettencourt & Geoffrey West, 2010. "A unified theory of urban living," Nature, Nature, vol. 467(7318), pages 912-913, October.
    6. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
    7. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
    8. Dion R J O’Neale & Shaun C Hendy, 2012. "Power Law Distributions of Patents as Indicators of Innovation," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-9, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luiz G A Alves & Renio S Mendes & Ervin K Lenzi & Haroldo V Ribeiro, 2015. "Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-17, September.
    2. Cardoso, M. & Souza, J.T.G. & Neli, R.R. & Souza, W.E., 2023. "Scaling laws from Brazilian state election results point out that, the candidate’s chance to win increases by investing more campaign efforts in smaller electorates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    3. Cardoso, M. & Silva, L.M.C. & Neli, R.R. & Souza, W.E., 2022. "Electorate involvement disorder: Universal relationship between the amplitude and electorate size in second round of Brazilian Presidential Election," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    4. Joao Meirelles & Camilo Rodrigues Neto & Fernando Fagundes Ferreira & Fabiano Lemes Ribeiro & Claudia Rebeca Binder, 2018. "Evolution of urban scaling: Evidence from Brazil," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-15, October.
    5. Mincheol Choi & Chang-Yang Lee, 2020. "Power-law distributions of corporate innovative output: evidence from U.S. patent data," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(1), pages 519-554, January.
    6. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Rodrigues, Francisco A., 2018. "Crime prediction through urban metrics and statistical learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 435-443.
    7. Cardoso, M. & Mendes, R.S. & Souza, J.T.G. & Ribeiro, H.V., 2020. "Gender difference in candidature processes for Brazilian elections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Luiz G A Alves & Haroldo V Ribeiro & Ervin K Lenzi & Renio S Mendes, 2013. "Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    2. Luiz G A Alves & Renio S Mendes & Ervin K Lenzi & Haroldo V Ribeiro, 2015. "Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-17, September.
    3. Huang, Siyu & Shi, Yi & Chen, Qinghua & Li, Xiaomeng, 2022. "The growth path of high-tech industries: Statistical laws and evolution demands," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    4. Yves Bettignies & Joao Meirelles & Gabriela Fernandez & Franziska Meinherz & Paul Hoekman & Philippe Bouillard & Aristide Athanassiadis, 2019. "The Scale-Dependent Behaviour of Cities: A Cross-Cities Multiscale Driver Analysis of Urban Energy Use," Sustainability, MDPI, vol. 11(12), pages 1-20, June.
    5. Yusra Ghafoor & Yi-Shin Chen & Kuan-Ta Chen, 2019. "Social Interaction Scaling for Contact Networks," Sustainability, MDPI, vol. 11(9), pages 1-14, May.
    6. Joao Meirelles & Camilo Rodrigues Neto & Fernando Fagundes Ferreira & Fabiano Lemes Ribeiro & Claudia Rebeca Binder, 2018. "Evolution of urban scaling: Evidence from Brazil," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-15, October.
    7. Brinkley, Catherine & Raj, Subhashni, 2022. "Perfusion and urban thickness: The shape of cities," Land Use Policy, Elsevier, vol. 115(C).
    8. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    9. Qingsong He & Lingping Huang & Jing Li, 2022. "Rediscovering the Scaling Law of Urban Land from a Multi-Scale Perspective—A Case Study of Wuhan," Land, MDPI, vol. 11(6), pages 1-15, June.
    10. Christian Düben & Melanie Krause, 2021. "Population, light, and the size distribution of cities," Journal of Regional Science, Wiley Blackwell, vol. 61(1), pages 189-211, January.
    11. David Levinson, 2012. "Network Structure and City Size," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-11, January.
    12. Didier Sornette & Thomas Maillart & Giacomo Ghezzi, 2014. "How Much Is the Whole Really More than the Sum of Its Parts? 1 ⊞ 1 = 2.5: Superlinear Productivity in Collective Group Actions," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-15, August.
    13. Somwrita Sarkar & Peter Phibbs & Roderick Simpson & Sachin Wasnik, 2015. "The scaling of income inequality in cities," Papers 1509.00959, arXiv.org.
    14. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    15. Dominik Hartmann & Flavio L. Pinheiro, 2022. "Economic complexity and inequality at the national and regional level," Papers 2206.00818, arXiv.org, revised Jun 2022.
    16. Haroldo V Ribeiro & Quentin S Hanley & Dan Lewis, 2018. "Unveiling relationships between crime and property in England and Wales via density scale-adjusted metrics and network tools," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-21, February.
    17. Anthony F J van Raan, 2013. "Universities Scale Like Cities," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-14, March.
    18. Kwok Tong Soo, 2018. "Innovation across cities," Journal of Regional Science, Wiley Blackwell, vol. 58(2), pages 295-314, March.
    19. Nir Kaplan & David Burg & Itzhak Omer, 2022. "Multiscale accessibility and urban performance," Environment and Planning B, , vol. 49(2), pages 687-703, February.
    20. Adam Okulicz-Kozaryn, 2022. "Materialism and Immorality: More Urban than Rural?," Societies, MDPI, vol. 12(5), pages 1-12, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:175-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.