Derivation of the distribution from extended Gibratʹs law

Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibratʹs law which holds in the middle profits region. From the law of detailed balance in all regions, Gibratʹs law in the high region and the non-Gibratʹs 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.