The improved algorithms to estimate α of alpha stable distribution based on empirical characteristic function

The estimation of characteristic exponent α is the most important step for the parameter estimation of symmetric α stable distribution. For lack of closed form of probability density function (pdf), classical methods are no longer available. In this paper improved algorithms based on the empirical characteristic function are proposed to solve this problem under the conditions of short data samples. Simulations show that the proposed algorithms are robust and they are more efficient and applicable than the conventional ones.