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

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  • Tomita, Shinji
  • Hayashi, Yukio

Abstract

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

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    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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