Comparing the Estimation Methods of Stable Distributions with Respect to Robustness Properties

Abstract

In statistical applications, some data set may exhibit the features like high skewness and kurtosis and heavy tailness that are incompatible with the normality assumption especially in finance and engineering. For these reason, the modeling of the data sets with alpha stable distributions will be reasonable approach. The stable distributions have four parameters. In literature, the estimation methods have been studied in order to estimate these unknown model parameters. In this study, we give small information about these proposed estimation methods and we compare these estimators with respect to robustness properties with a comprehensive simulation study, since the robustness property of an estimator has been an important tool for an appropriate modeling.