  Starting from a master equation, we derive the evolution equation for the
size distribution of elements in an evolving system, where each element can
grow, divide into two, and produce new elements. We then probe general
solutions of the evolution quation, to obtain such skew distributions as
power-law, log-normal, and Weibull distributions, depending on the growth or
division and production. Specifically, repeated production of elements of
uniform size leads to power-law distributions, whereas production of elements
with the size distributed according to the current distribution as well as no
production of new elements results in log-normal distributions. Finally,
division into two, or binary fission, bears Weibull distributions. Numerical
simulations are also carried out, confirming the validity of the obtained
solutions.
