Articles in peer-reviewed journals
|How skew distributions emerge in evolving systems|
|Choi M.Y., Choi H., Fortin J.-Y. and Choi J.|
|Europhysics Letters 85 (2009) 30006|
|DOI : 10.1209/0295-5075/85/30006|
Despite the ubiquitous emergence of skew distributions such as power-law, log-normal, and Weibull distributions, in a variety of evolving systems, there still lacks proper understanding of the mechanism as well as relations bet ween them. It is studied how such distributions emerge in general evolving systems and what makes the difference between them. Beginning with a master equation for general evolving systems, we obtain the time evolution equation for the size distribution function. Obtained in the case of size changes proportional to the current size for the Yule-type transition rate are the power-law stationary distribution with an arbitrary exponent and the evolving distribution, which is of either log-normal or Weibull type asymptotically, depending on production and growth in the system. This master equation approach thus gives a unified description of those three ty pes of skew distribution observed in a variety of systems, providing physical derivation of them and disclosing how they are related.