IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.13781.html

Distribution in the Geometrically Growing System and Its Evolution

Author

Listed:
  • Kim Chol-jun

Abstract

Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without introduction of delicate economic models but only on the statistical way. A convexity in the low-size part of the distribution is one peculiarity of the theory, which is absent in the power-law distribution. We found that the distribution of the geometrically growing system could have a trend to flatten in the evolution of the system so that the relative ratio of size within the system increases. The system can act as a reverse machine to covert a diffusion in parametric space to a concentration in the size distribution.

Suggested Citation

  • Kim Chol-jun, 2023. "Distribution in the Geometrically Growing System and Its Evolution," Papers 2302.13781, arXiv.org.
    • Handle: RePEc:arx:papers:2302.13781
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.13781
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    2. Ioannides, Yannis & Skouras, Spyros, 2013. "US city size distribution: Robustly Pareto, but only in the tail," Journal of Urban Economics, Elsevier, vol. 73(1), pages 18-29.
    Full references (including those not matched with items on IDEAS)

    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. Unchitta Kan & Jericho McLeod & Eduardo López, 2024. "Non-coresident family as a driver of migration change in a crisis: the case of the COVID-19 pandemic," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 11(1), pages 1-11, December.
    2. González-Val, Rafael, 2019. "Lognormal city size distribution and distance," Economics Letters, Elsevier, vol. 181(C), pages 7-10.
    3. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    4. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2024. "Mixtures of log-normal distributions in the mid-scale range of firm-size variables," Evolutionary and Institutional Economics Review, Springer, vol. 21(2), pages 249-260, September.
    5. Sen, Hu & Chunxia, Yang & Xueshuai, Zhu & Zhilai, Zheng & Ya, Cao, 2015. "Distributions of region size and GDP and their relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 46-56.
    6. Rafael González-Val, 2021. "The Probability Distribution of Worldwide Forest Areas," Sustainability, MDPI, vol. 13(3), pages 1-19, January.
    7. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    8. Calderín-Ojeda, Enrique, 2016. "The distribution of all French communes: A composite parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 385-394.
    9. Hasan Engin Duran & Andrzej Cieślik, 2021. "The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(5), pages 1702-1719, October.
    10. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    11. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    12. Davis, Richard & Ng, Serena, 2023. "Time series estimation of the dynamic effects of disaster-type shocks," Journal of Econometrics, Elsevier, vol. 235(1), pages 180-201.
    13. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    14. 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.
    15. Desmet, Klaus & Henderson, J. Vernon, 2015. "The Geography of Development Within Countries," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 1457-1517, Elsevier.
    16. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
    17. Marco Bee, 2020. "On discriminating between lognormal and Pareto tail: A mixture-based approach," DEM Working Papers 2020/9, Department of Economics and Management.
    18. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    19. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.
    20. Chengri Ding & Zhi Li, 2019. "Size and urban growth of Chinese cities during the era of transformation toward a market economy," Environment and Planning B, , vol. 46(1), pages 27-46, January.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2302.13781. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.