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Mixtures of log-normal distributions in the mid-scale range of firm-size variables

Author

Listed:
  • Arturo Ramos

    (Universidad de Zaragoza)

  • Till Massing

    (Universität Duisburg-Essen)

  • Atushi Ishikawa

    (Kanazawa Gakuin University)

  • Shouji Fujimoto

    (Kanazawa Gakuin University)

  • Takayuki Mizuno

    (National Institute of Informatics
    The Graduate University for Advanced Studies [SOKENDAI]
    The University of Tokyo)

Abstract

In econophysics, firm sales and other firm-size variables follow a power-law distribution in the large-scale range and a log-normal distribution in the mid-scale range. Employing sales (operating revenues) data, we statistically tested the validity of this assertion by applying log-normal distributions and mixtures of them to the comprehensive data available in ORBIS, the world’s largest commercial database on corporate finance. The results confirm that the validity of explaining the entire range of firm-size variables with a single log-normal distribution is extremely low. We also confirmed the statistical superiority of the mid-scale range, which conventionally follows a single log-normal distribution in econophysics, described as a mixture of three log-normal distributions. This result is likely due to the observed effect of the superposition of at least a few industries, such as manufacturing, non-manufacturing, and others.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eaiere:v:21:y:2024:i:2:d:10.1007_s40844-024-00283-1
    DOI: 10.1007/s40844-024-00283-1
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    References listed on IDEAS

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    More about this item

    Keywords

    Log-normal; Mixtures; Firm-size distribution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D39 - Microeconomics - - Distribution - - - Other
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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