P-Order Normal Cloud Model: Walking on the Way between Gaussian and Power Law Distributions

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.