Parameter estimation of positive alpha-stable distribution based on negative-order moments

Positive alpha-stable distribution is used to model the non-negative quantity with impulsive property. Based on negative-order moments, three methods are used to estimate the parameters of positive alpha-stable distribution in this paper. First, a ratio estimator based on the ratio of negative-order moments is presented whose performance is significantly determined by the choice of order. Second, a new estimator with explicit closed form is presented and it is shown to be robust compared to the ratio estimator. Last, an iterative estimator is proposed and it achieves better performance only using fewer samples in each step computation. Monte Carlo simulation results demonstrate that the proposed iterative estimator is high efficient for the positive alpha-stable distribution.