Study on the Statistical Distribution of Returns Series

Stable distribution is far-ranging employed in finance. In this paper, we applied the way of characteristic function in the stable distribution to fit the Shanghai Stocks Exchange Composite index, and some skills were provided. It turned out that, stable distribution was very well in fitting the empirical distribution, which displays the peaks higher and the tails heavier. And it possesses the additives property of normal distribution. So stable can plot the real action of financial remarket, it is well applied to ask accurate distribution such as the technology of risk management, the theory of portfolio investment.