Robust correlation coefficient goodmness-of-fit test for the extreme value distribution

A simple robust method is provided to test the goodness of fit for the extreme value distribution (Type I family) by using the new diagnostic tool called the Forward Search method. The Forward Search is a powerful general method that provides diagnostic plots for finding outliers and discovering their underlying effects on models fitted to the data and for assessing the adequacy of the model. The Forward Search algorithm has been previously developed for regression modeling and multivariate analysis frameworks. One of the powerful goodness-of-fit tests is represented by the correlation coefficient test, but this test suffers from the presence of outliers. We introduce the Forward Search version of this test that is not affected by the outliers. Also by using the transformation study, an application to the two-parameter Weibull distribution is investigated. The performance and the ability of this procedure to capture the structure of data are illustrated by some simulation studies