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A controllable model of a random multiplicative process for the entire distribution of population


  • Tomita, Shinji
  • Hayashi, Yukio


A random multiplicative process (RMP) is one of the basic models which can generate a power law distribution. Actually, the distribution generated by RMP has two parts, which are closely matched to the head of a log-normal distribution and the tail of a power law distribution. We investigated the relation between shapes of distributions and model variables. By changing input variables, we explained the origin of the cumulative population distributions of municipalities and prefectures in Japan from 1980 to 2006. This controllability of RMP can be applied to a power law distribution in various other fields.

Suggested Citation

  • Tomita, Shinji & Hayashi, Yukio, 2008. "A controllable model of a random multiplicative process for the entire distribution of population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1345-1351.
  • Handle: RePEc:eee:phsmap:v:387:y:2008:i:5:p:1345-1351
    DOI: 10.1016/j.physa.2007.09.028

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    References listed on IDEAS

    1. Glaeser, Edward L. & Scheinkman, JoseA. & Shleifer, Andrei, 1995. "Economic growth in a cross-section of cities," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 117-143, August.
    2. Eaton, Jonathan & Eckstein, Zvi, 1997. "Cities and growth: Theory and evidence from France and Japan," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 443-474, August.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. repec:hoo:wpaper:e-95-4 is not listed on IDEAS
    5. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
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    Cited by:

    1. Cura, Robin & Cottineau, Clémentine & Swerts, Elfie & Ignazzi, Cosmo Antonio & Bretagnolle, Anne & Vacchiani-Marcuzzo, Celine & Pumain, Denise, 2017. "The Old and the New: Qualifying City Systems in the World with Classical Models and New Data," SocArXiv pbzn6, Center for Open Science.


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