Estimating the skewness parameter of a Levy-stable

Abstract

Stable distributions consist in probability models that are described by four parameters for the shape, location, scale and skewness. These parameters were estimated by several classical methods. Recently, the extreme value theory were exploited to propose estimators to the first three. In this paper, we use the same technique to introduce an estimator to the skewness parameter. We carry out a simulation study to evaluate its performance by computing estimation biases and mean squared errors and providing bootstrap confidence bounds as well.