Abstract
Gaussian and power law distribution are two important distribution types. Gaussian distribution is widely spread in nature phenomenon. Most things which obey power law distribution are man-made. We studied the relationship between Gaussian and power law distribution, and gave a new distribution model, is called P-order normal cloud model, of which we proved the basic statistic characteristic. We count distribution law of P-order normal cloud model by experimentation. Then we found a)when P=1, the model obeys Gaussian distribution; 2)with P increased, the characteristics of Gaussian distribution will gradually disappeared, then samples are sharply closed to mean value, but few samples which are distant from mean value are evenly distributed. 3) The samples distribution pattern of high-order normal cloud model(when P>5) reflects power law characteristics.
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References
Bolthausen, E., Deuschel, J.D., Zeitouni, O.: Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field. Elect. Comm. in Probab. 16, 114–119 (2011)
Lindgren, F., Rue, H., Lindstrom, J.: An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73, 423–498 (2011)
Lawrence, N.D., Jordan, M.I.: Semi-supervised learning via Gaussian processes. In: NIPS (2004)
Adamic, L.A., Huberman, B.A.: Power-law distribution of the world wide web. Science 287, 2115 (2000)
Haro, M., Serrà , J., Corral, A., Herrera, P.: Power-law distribution in encoded MFCC frames of speech, music, and environmental sound signals. In: 21st International World Wide Web Conference, pp. 895–902. ACM, Lyon (2012)
Brantle, T.F., Fallah, M.H.: Complex innovation networks, patent citations and power laws. In: PICMET, pp. 540–549. IEEE (2007)
Li, D., Du, Y.: Artificial intelligence with uncertainty. Chapman & Hall/CRC (2007)
Wang, L.: Normal Cloud Model Mathematical Properties and Cloud Filter. Personal Communication (2011)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press, England (1992)
Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009)
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Liu, Y., Zhang, T. (2012). P-Order Normal Cloud Model: Walking on the Way between Gaussian and Power Law Distributions. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34481-7_57
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DOI: https://doi.org/10.1007/978-3-642-34481-7_57
Publisher Name: Springer, Berlin, Heidelberg
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