  We report the proof that the expression of extended Gibrat's law is unique
and the probability distribution function (pdf) is also uniquely derived from
the law of detailed balance and the extended Gibrat's law. In the proof, two
approximations are employed that the pdf of growth rate is described as
tent-shaped exponential functions and that the value of the origin of growth
rate 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.
