A Goodness-of-Fit Test for the Gumbel Distribution Based on Kullback–Leibler Information

Abstract

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.

Keywords:

• Entropy
• Monte Carlo simulation
• Test power

Mathematics Subject Classification:

• Primary 62G10
• Secondary 62Q05

Acknowledgment

The authors wish to express their thanks to an anonymous referee for his constructive comments which helped to improve the presentation of the original version of this article.