On Tests for Distinguishing Distribution Tails

We propose a test procedure for distinguishing between two separable classes of arbitrary distribution tails and, moreover, prove its consistency. The method is based on the goodness-of-fit test for an arbitrary distribution tail, and properties of this test are also discussed. This is the first goodness-of-fit test for distribution tails proposed in the literature that can be applied for testing the goodness-of-fit hypothesis with a discrete distribution tail. In contrast to the over-whelming majority of works related to statistics of extremes, we do not assume that the distributions belong to any of maximum domains of attraction.