针对在复杂性系统研究中幂律分布扮演着越来越重要的角色而又不存在公认的合理导出的矛盾,基于复杂性系统的不可解性,在非完整统计的思想基础上,分别在归一化条件、统计平均和Shannon熵的方程中引入不同的指数因子,由最大熵原理推导出了指数函数、幂函数和幂函数与指数函数乘积形式的概率分布函数;展现了由Shannon熵和最大熵原理推导等概率假设的过程;同时也展现了可导出指数分布、幂律分布和幂函数与指数函数乘积形式分布的一种新机制,即最大熵原理。
For resolving the contradiction between power-law distribution playing an increasingly important role in investigation of complex systems and it has not been derived out up to now, in this paper the maximal entropy principle and the idea of incomplete statistics were utilized. Firstly, the detail of deriving the equal probability hypothesis from Shannon entropy and maximum entropy principle was showed. Then three different exponential factors were introduced in equations about the normalization condition, statistical average and Shannon entropy respectively. Based on the Shannon entropy and maximum entropy principle, three different probability distribution functions, such as exponential function, power function and the product form consisting of power function and exponential function, were derived out. Which demonstrated the maximum entropy principle was a path which may lead to different distribution functions.
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