The uniqueness of company size distribution function from tent-shaped growth rate distribution

Details The uniqueness of company size distribution function from tent-shaped growth rate distribution The uniqueness of company size distribution function from tent-shaped growth rate distribution

2007-02-28

arxiv.org/abs/physics/0702248v1

Physics

Physics and Society

6 pages, 5 figures

Scientific paper

10.1016/j.physa.2007.04.089

We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-shaped exponential functions and the value of the origin of the growth rate distribution is constant. These approximations are confirmed in profits data of Japanese companies 2003 and 2004. The resultant profits pdf fits with the empirical data with high accuracy. This guarantees the validity of the approximations.

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