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Abstract: Employing profits data of Japanese firms in 2003-2005, we kinematicallyexhibit the static log-normal distribution in the middle scale region. In thederivation, a Non-Gibrat-s law under the detailed balance is adopted togetherwith following two approximations. Firstly, the probability density function ofprofits growth rate is described as a tent-shaped exponential function.Secondly, the value of the origin of the growth rate distribution divided intobins is constant. The derivation is confirmed in the database consistently.This static procedure is applied to a quasi-static system. We dynamicallydescribe a quasi-static log-normal distribution in the middle scale region. Inthe derivation, a Non-Gibrat-s law under the detailed quasi-balance is adoptedtogether with two approximations confirmed in the static system. The resultantdistribution is power-law with varying Pareto index in the large scale regionand the quasi-static log-normal distribution in the middle scale region. In thedistribution, not only the change of Pareto index but also the change of thevariance of the log-normal distribution depends on the parameter of thedetailed quasi-balance. As a result, Pareto index and the variance of thelog-normal distribution are related to each other.



Autor: Atushi Ishikawa

Fuente: https://arxiv.org/







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