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

Arturo Ramos, Till Massing (), Atushi Ishikawa (), Shouji Fujimoto () and Takayuki Mizuno ()
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Till Massing: Universität Duisburg-Essen
Atushi Ishikawa: Kanazawa Gakuin University
Shouji Fujimoto: Kanazawa Gakuin University
Takayuki Mizuno: National Institute of Informatics

Evolutionary and Institutional Economics Review, 2024, vol. 21, issue 2, No 8, 249-260

Abstract: 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.

Keywords: Log-normal; Mixtures; Firm-size distribution (search for similar items in EconPapers)
JEL-codes: C61 D39 L25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40844-024-00283-1

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