Characteristic function based estimation of stable distribution parameters
A practical guide to heavy tails
Numerical approximation of the symmetric stable distribution and density
A practical guide to heavy tails
An algorithm for evaluating stable densities in Zolotarev's (M) parameterization
Mathematical and Computer Modelling: An International Journal
Maximum likelihood estimation of stable Paretian models
Mathematical and Computer Modelling: An International Journal
IEEE Transactions on Communications
α-stable interference modeling and cauchy receiver for an IR-UWB ad hoc network
IEEE Transactions on Communications
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Fitting general stable laws to data by maximum likelihood is important but difficult. This is why much research has considered alternative procedures based on empirical characteristic functions. Two problems then are how many values of the characteristic function to select, and how to position them. We provide recommendations for both of these topics. We propose an arithmetic spacing of transform variables, coupled with a recommendation for the location of the variables. It is shown that arithmetic spacing, which is far simpler to implement, closely approximates optimum spacing. The new methods that result are compared in simulation studies with existing methods, including maximum-likelihood. The main conclusion is that arithmetic spacing of the values of the characteristic function, coupled with appropriately limiting the range for these values, improves the overall performance of the regression-type method of Koutrouvelis, which is the standard procedure for estimating general stable law parameters.