In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce...

It is shown that Gaussian mixture distributions cannot be distinguished from Laplace distributions and that the scaling relationship between the standard deviation of growth rates and the size of the firms is likely to be an artefact. A novel homogeneous dataset confirms both results.

The daily financial volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well to their long-term trends. We also model the transition to a Gaussian distribution for longer time intervals, like months instead of days.

In this paper, a new approximate formula to probability integral is deduced using theoretical analysis combining with computer numerical simulation. The absolute storage capacity of the Hopfield neural network is analyzed with this approximate formula and a more strict result is obtained.