A Goodness-of-Fit Test for the Gumbel Distribution Based on Kullback–Leibler Information
A goodness-of-fit test for the Gumbel distribution is proposed. This test is based on the Kullback–Leibler discrimination information methodology proposed by Song (2002). The critical values of the test were obtained by using Monte Carlo simulation for small sample sizes and different levels of significance. The proposed test is compared with the tests developed by Stephens (1977), Chandra et al. (1981), and the test given by Kinnison (1989) in terms of their power by considering various alternative distributions. Simulation results show that the Kullback–Leibler information test has higher power than some of the studied tests.