The identification of outliers in exponential samples

In this paper the task of identifying outliers in exponential samples is treated conceptionally in the sense of Davies and Gather (1989, 1993) by means of a so called outlier region. In case of an exponential distribution, an empirical approximation of such a region also called an outlier identifier is mainly dependent on some estimator of the unknown scale parameter. The worst case behaviour of several reasonable outlier identifiers is investigated thoroughly and it is shown that only robust estimators of scale should be used to construct reliable identifiers. These findings lead to the recommendation of an outlier identifier that is based on a standardized version of the sample median.