A Goodness-of-Fit Test for Location-Scale Max-Stable Distributions

Abstract

In this article, a technique based on the sample correlation coefficient to construct goodness-of-fit tests for max-stable distributions with unknown location and scale parameters and finite second moment is proposed. Specific details to test for the Gumbel distribution are given, including critical values for small sample sizes as well as approximate critical values for larger sample sizes by using normal quantiles. A comparison by Monte Carlo simulation shows that the proposed test for the Gumbel hypothesis is substantially more powerful than some other known tests against some alternative distributions with positive skewness coefficient.

Keywords:

• Correlation coefficient
• Extreme value distributions
• Hypothesis testing
• Location-scale invariant statistic

Mathematics Subject Classification:

• 62G10
• 62G32
• 62Q05
• 62E17