Proof of the heavy tailed property of normal cloud model

2011, Volume 13, Issue 4

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Strategic Study of CAE >> 2011, Volume 13, Issue 4

Proof of the heavy tailed property of normal cloud model

1.Institute of Electronic System Engineering, Beijing 100840, China;

2 .Institute of Command Automation,PLA University of Science and Technology, Nanjing 210007, China

Funding project：国家自然科学基金资助项目（60974086）；国家“973”资助项目（2007CB311003） Received: 2011-01-20 Available online: 2011-04-08 12:00:17.000

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Abstract

Normal distribution and heavy tailed distribution are very important in probability theories. They have totally different mathematical forms and physical meanings. The probability density function of normal distribution decay exponentially to 0. The majority of normal random variable values are around the mathematical expectation. The tailed distribution function of the random variables that obey heavy tailed distribution shows heavy tailed characteristic. The probability density function decays power exponentially to 0.In this paper, we proved that the normal cloud model is heavy tailed distribution and its mathematical expectation exists.It is intermediate between notmal distribution and heavy tailed distribution. The parameter He(hyper entropy) of the normal cloud model is the bridge from normal distribution to heavy tailed distribution.

Keywords

normal distribution ; heavy tailed distribution ; normal cloud model ; kurtosis

References

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