PROPERTIES OF SELECTED SIGNIFICANCE TESTS FOR EXTREME VALUE INDEX

Abstract

The paper presents two tests verifying the hypothesis about the shape parameter of the generalized distribution of maximum statistic. It is called the extreme value index. The inverse of the positive index is called the tail index and determines the degree of fatness of the tail. The asymptotic properties of the Pickands and the Hill estimator of the shape parameter are used to construct the test statistics. Simulation studies of the properties of these significance tests allow us to formulate some conclusions regarding their applications.

Keywords

• extreme index, size of test, power of test, Pickands estimator, Hill estimator