Homogeneity tests based upon Gumbel distribution and a critical appraisal of Dalrymple's test

Homogeneity tests are an important component of many regional flood frequency analysis methods, particularly index flood methods. The index flood method was first suggested by Dalrymple, who also proposed a homogeneity test. Dalrymple's test has been widely used in hydrologic practice for more than 30 years. This paper analyzes the relative performance of Dalrymple's test, a normalized quantile test based upon L-moment parameter estimation (X-10 test), and a method of moment Cν test (MoM-Cν test). Dalrymple's original test is shown to be in error and a corrected version is developed. A Monte Carlo study compares the power of these three tests, after applying correction factors to the test statistics to achieve a 5% Type I error. The L-moment X-10 test was always more powerful then Dalrymple's test or the MoM-Cν test. Moreover, the X-10 test needs much less correction to achieve the specified Type I error. An analytical analysis of the power of the tests is consistent with the Monte Carlo results. The superior performance of the X-10 test is due to its L-moment estimation procedure, which yields a smaller sampling variance and a sampling distribution closer to normality than classical product moments. The relationship of the X-10 test with other L-moment based tests proposed by other workers is discussed. The original version of Dalrymple's test should not be used.