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Since alpha-stable distribution was introduced as a generalization of Gaussian distribution, it has been applied widely in wireless communication field, such as designing filter, modeling impulsive noises and so on. In this paper, parameter estimation methods of alpha-stable distribution are classified into five types and a classic method in each type is studied based on our analysis. Specially, two important results are presented: After sample number increases to 213, precision of MLE based on FFT is not improved much; with alphararr2 , error of estimation for alpha in extreme value method is growing, which are neglected in the past researches. Finally, Monte-Carlo simulations are used to verify results.