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

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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.

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Data availability statement

We purchased the 2016 ORBIS database from Bureau van Dijk. Since we signed a confidentiality agreement, we are not allowed to disclose the data sets. For the sake of replication, interested researchers can buy the same edition of such database.

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Author information

Authors and Affiliations

  1. Departmento de Análisis Económico, Universidad de Zaragoza, Zaragoza, Spain

    Arturo Ramos

  2. Fakultät für Wirtschaftswissenschaften, Lehrstuhl für Ökonometrie, Universität Duisburg-Essen, Essen, Germany

    Till Massing

  3. Department of Information Engneering, Kanazawa Gakuin University, Kanazawa, Japan

    Atushi Ishikawa & Shouji Fujimoto

  4. National Institute of Informatics, Tokyo, Japan

    Takayuki Mizuno

  5. The Graduate University for Advanced Studies [SOKENDAI], Tokyo, Japan

    Takayuki Mizuno

  6. Center for Advanced Research in Finance, The University of Tokyo, Tokyo, Japan

    Takayuki Mizuno

Authors
  1. Arturo Ramos
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  2. Till Massing
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  3. Atushi Ishikawa
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  4. Shouji Fujimoto
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  5. Takayuki Mizuno
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Contributions

Arturo Ramos: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, resources, software, validation, visualization, writing-original draft. Till Massing: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, software, supervision, validation, visualization, writing-original draft. Atushi Ishikawa: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, software, supervision, validation, visualization, writing-original draft. Shouji Fujimoto: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, software, supervision, validation, visualization, writing-original draft. Takayuki Mizuno: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, software, supervision, validation, visualization, writing-original draft.

Corresponding author

Correspondence to Atushi Ishikawa.

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The authors declare no Conflict of interest concerning the research carried out in this article.

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This study was supported by JSPS KAKENHI Grant Numbers 21K04557, 21H01569, and 22K04609, by Deutsche Forschungsgemeinschaft (DFG) Grant Number 455257011, by PID2020-112773GB-I00 of the Spanish Ministerio de Ciencia e Innovación, and by the ADETRE Reference Group S39_20R of Gobierno de Aragón..

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Ramos, A., Massing, T., Ishikawa, A. et al. Mixtures of log-normal distributions in the mid-scale range of firm-size variables. Evolut Inst Econ Rev (2024). https://doi.org/10.1007/s40844-024-00283-1

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