Closed-form estimator for widening valid estimation range of Pareto parameter

The second order moment of the multi-look Pareto distribution is invalid when the shape parameter is less than 2, so the method of the first two moments cannot estimate the shape parameter less than 2. This paper proposes the method for estimating the shape parameter of multi-look Pareto distribution. The method not only widens the valid range of parameter estimation, but also the expression for estimation is closed. Theoretical analysis and experiment both prove that the method can estimate shape parameter less than 1 compared with the method of moments and that costs are lower in computation than the method of fractional moments.