Statistical choice of extremal models for complete and censored data

Abstract

Within the framework of the general extreme-value distribution (GEV, with shape parameter θ), which combines the Fréchet (θ < 0), Gumbel (θ = 0) and Weibull types (θ > 0), the power functions of some statistics for rejecting the Gumbel distribution (θ = 0) are compared. Often in checking the suitability of a distribution, a goodness of fit test is used involving the whole range of the distribution whilst the valid interest is in one tail only. The influence of the observations in the other tail on the power of the test is evaluated and the correctness of the distribution in that other tail of the sample is discussed. © 1985.