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

Employing profits data of Japanese firms in 2003 and 2004, we report the proof that a Non-Gibrat's law in the middle scale region of profits is unique under the law of detailed balance. This uniquely leads to the probability distribution function (pdf) of profits. 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 the database. The resultant profits pdf fits with the empirical data consistently. This guarantees the validity of the approximations.