  The purpose of this paper is to construct a new non-parametric detector of
univariate outliers and to study its asymptotic properties. This detector is
based on a Hill's type statistic. It satisfies a unique asymptotic behavior 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 have illustrated our results by numerical
simulations which show the accuracy of this detector with respect to other
usual univariate outlier detectors (Tukey, MAD or Local Outlier Factor
detectors). The detection of outliers in a database providing the prices of
used cars is also proposed as an application to real-life database.
