How skew distributions emerge in evolving systems

摘要: Despite the ubiquitous emergence of skew distributions such as power law, log-normal, and Weibull distributions, there still lacks proper understanding mechanism well relations between them. It is studied how emerge in general evolving systems what makes difference Beginning with a master equation for systems, we obtain time evolution size distribution function. Obtained case changes proportional to current are law stationary an arbitrary exponent distribution, which either log-normal or type asymptotically, depending on production growth system. This approach thus gives unified description those three types observed variety providing physical derivation them disclosing they related.