On testing that the distribution of extremes is of type I when type II is the alternative

Abstract

Distributions of largest extremes are normally used to estimate tail probabilities. When dealing with unlimited extremes, the question arises which type of distributions of extremes is adequate. Sometimes the Gumbel distribution (type I), which can be regarded as a restriction of the log-Gumbel distribution (type II), is used without sufficient support for this choice; estimated extreme tail probabilities can then be more influenced by the choice of the type than by the data. This paper gives a quick test with high power where type I is the null hypothesis and type II is the alternative; it is a result based on a study to be published elsewhere dealing with the reduction of power as a consequence of using numerically simplified tests.