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| A Mechanism of Generating Power-Law and Other Distributions |
| LI Heling1,2, WANG Juanjuan1, YANG Bin1,2, SHEN Hongjun1,2
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1. School of Physics and Electrical Information Science, Ningxia University, Yinchuan 750021, China;
2. Key Lab on Information Sensing and Intelligent Desert, Yinchuan 750021, China |
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Abstract 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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Received: 20 January 2015
Published: 25 February 2025
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