L-MOMENT AND PROBABILITY PLOT CORRELATION-COEFFICIENT GOODNESS-OF-FITTESTS 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 d istribution 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) us ing unbiased PWM estimators. The generalized extreme value (GEV) distr ibution with various values of the shape parameter kappa was used as t he parent distribution. Results show that the L moment-based tests out perform the PPCC test for independent data, or data with small autocor relations (rho less than or equal to 0.4). For high autocorrelation (r ho = 0.8), all tests are invalid because the type 1 error probability is larger than the target value. An example demonstrates consistency p roblems with scale and shape parameters estimated using the biased PWM estimators; these cause us to advise against their use and to recomme nd instead unbiased PWM estimators that employ a sample's order statis tics. Overall, this paper provides another endorsement of the use of u nbiased L moment estimators for goodness-of-fit tests and distribution selection, as well as a recommendation for parameter estimation.