Derivation of the distribution from extended Gibrat's law

Abstract

Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's law in the high region and the non-Gibrat's law in the middle region, we kinematically derive the profits distribution function in the high and middle range uniformly. The distribution function accurately fits with empirical data without any fitting parameter.

arXiv comment13 pages, 8 figures

References in corpus (10)

• Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States
• Universal features in the growth dynamics of complex organizations
• Power Law Scaling for a System of Interacting Units with Complex Internal Structure
• Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms
• Growth and Fluctuations of Personal Income
• Scaling behavior in economics: II. Modeling of company growth
• Pareto index induced from the scale of companies
• Pareto law and Pareto index in the income distribution of Japanese companies
• Fractal Structure with a Typical Scale
• Relations between a typical scale and averages in the breaking of fractal distribution

Cited by in corpus (4)

• The uniqueness of company size distribution function from tent-shaped growth rate distribution
• Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance
• Fat-tailed fluctuations in the size of organizations: the role of social influence
• Shape of Growth Rate Distribution Determines the Type of Non-Gibrat's Property