On the estimation of the parameters of α-stable distributions using linear regression in the characteristic function domain

It has been shown previously that parameter estimation of stable distributions can be effectively performed through a regression procedure on the empirical characteristic function (ECF). An alternative, using the kernel characteristic function estimator (KCFE), is proposed and is shown to provide superior performance under some conditions. Additionally, it is found that defining a truncated regression region as the span where the variance of the ECF is below a threshold, can be used to circumvent the need for tabulated values to achieve good estimates