L-MOMENT 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-Cs test suggested by Chowdhury et al. (1991) using unbiased PWM estimators. The generalized extreme value (GEV) distribution with various values of the shape parameter kappa 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 (rho less than or equal to 0.4). For high autocorrelation (rho = 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.