A new non-parametric detector of univariate outliers for distributions with positive unbounded support

The purpose of this paper is the construction and the asymptotic property study of a new non-parametric detector of univariate outliers. This detector, based on a Hill's type statistics, is valid for a large set of probability distributions with positive unbounded support, for instance for the absolute value of Gaussian, Gamma, Weibull, Student or regular variations distributions. We illustrate our results by numerical simulations which show the accuracy of this detector with respect to other usual univariate outlier detectors (Tukey, MADE or Local Outlier Factor detectors). An application to real-life data allows to detect outliers in a database providing the prices of used cars.