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Abstract
In this paper we will survey Hills estimator, which is one of the most popular estimators for the tail index of heavy-tailed distributions. Applications are numerous and include, for example, insurance reliability theory, econometrics, geology and cli-matology. We will outline how Hills estimator is constructed and summarize the developments of its properties like consistency and asymptotic normality. Therefore, we will introduce the concept of first- and second-order regular variation. Further-more, we will give an overview of proposed methods for choosing the number of order statistics, a very crucial parameter in Hills estimator. Graphical tools for the estimator will be illustrated on the basis of an example.