Approximate goodness-of-fit tests of fitted generalized extreme value distributions using LH moments

Abstract

Approximate goodness-of-fit tests of fitted generalized extreme value (GEV) distributions using LH moments are formulated on the basis of comparison of sample LH kurtosis estimates and theoretical LH kurtosis values of the fitted distributions. These tests are different from those that have been derived for testing the GEV distributions of which parameter values are known a priori. The tests are intended to answer the following questions: Does a fitted GEV distribution describe adequately a given data series? If not, can the GEV distribution function describe adequately the larger events in that data series for use for high quantile estimation? If so, what degree of emphasis on the larger events is needed in order that the GEV distribution becomes acceptable? The use of the GEV distribution in conjunction with the LH moment estimation method and the formulated tests should alleviate the need for finding the 'correct' distribution. The tests are evaluated by Monte Carlo simulations using generated samples of both GEV and Wakeby distributions. Applications of the tests to observed annual maximum streamflow data are presented.