IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i22p5598-5610.html
   My bibliography  Save this article

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

Author

Listed:
  • Eliazar, Iddo I.
  • Cohen, Morrel H.

Abstract

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.

Suggested Citation

  • Eliazar, Iddo I. & Cohen, Morrel H., 2012. "A Langevin approach to the Log–Gauss–Pareto composite statistical structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5598-5610.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5598-5610
    DOI: 10.1016/j.physa.2012.06.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112005286
    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.2012.06.024?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. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    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. Luckstead, Jeff & Devadoss, Stephen, 2017. "Pareto tails and lognormal body of US cities size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 573-578.
    2. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.
    3. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.

    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. Mercik, Szymon & Weron, Rafal, 2002. "Origins of scaling in FX markets," MPRA Paper 2294, University Library of Munich, Germany.
    2. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    3. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    4. Sabrina Camargo & Silvio M. Duarte Queiros & Celia Anteneodo, 2013. "Bridging stylized facts in finance and data non-stationarities," Papers 1302.3197, arXiv.org, revised May 2013.
    5. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    6. Laleh Tafakori & Armin Pourkhanali & Riccardo Rastelli, 2022. "Measuring systemic risk and contagion in the European financial network," Empirical Economics, Springer, vol. 63(1), pages 345-389, July.
    7. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    8. 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.
    9. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    10. Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    11. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    12. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.
    13. Kutner, Ryszard & Wysocki, Krzysztof, 1999. "Applications of statistical mechanics to non-brownian random motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 67-84.
    14. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    15. Lee, Jae Woo & Eun Lee, Kyoung & Arne Rikvold, Per, 2006. "Multifractal behavior of the Korean stock-market index KOSPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 355-361.
    16. Zhang, J.W. & Zhang, Y. & Kleinert, H., 2007. "Power tails of index distributions in chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 166-172.
    17. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    18. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    19. Chakrabarti, Anindya S., 2015. "Stochastic Lotka-Volterra equations: A model of lagged diffusion of technology in an interconnected world," IIMA Working Papers WP2015-08-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    20. David Vidal-Tomás & Simone Alfarano, 2020. "An agent-based early warning indicator for financial market instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 49-87, January.

    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:391:y:2012:i:22:p:5598-5610. 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.