  We introduce a stochastic model to explain a double power-law distribution
which exhibits two different Paretian behaviors in the upper and the lower tail
and widely exists in social and economic systems. The model incorporates
fitness consideration and noise fluctuation. We find that if the number of
variables (e.g. the degree of nodes in complex networks or people's incomes)
grows exponentially, normal distributed fitness coupled with exponentially
increasing variable is responsible for the emergence of the double power-law
distribution. Fluctuations do not change the result qualitatively but
contribute to the second-part scaling exponent. The evolution of Chinese
airline network is taken as an example to show a nice agreement with our
stochastic model.
