LMoment and Probability Plot Correlation Coefficient Goodness‐of‐fit Tests for the Gumbel Distribution and Impact of Autocorrelation

This paper analyzes the power of two L moment and the probability plot correlation coefficient (PPCC) goodness‐of‐fit tests for the Gumbel distribution and the impact of autocorrelation. The two L moment tests are the kappa test suggested by Hosking et al. (1985) using biased PWM estimators, and the L ‐ C s test suggested by Chowdhury et al. (1991) using unbiased PWM estimators. The generalized extreme value (GEV) distribution with various values of the shape parameter κ was used as the parent distribution. Results show that the L moment‐based tests outperform the PPCC test for independent data, or data with small autocorrelations (ρ ≤ 0.4). For high autocorrelation (ρ = 0.8), all tests are invalid because the type 1 error probability is larger than the target value. An example demonstrates consistency problems with scale and shape parameters estimated using the biased PWM estimators; these cause us to advise against their use and to recommend instead unbiased PWM estimators that employ a sample's order statistics. Overall, this paper provides another endorsement of the use of unbiased L moment estimators for goodness‐of‐fit tests and distribution selection, as well as a recommendation for parameter estimation.