Establishing acceptance regions for L-moments based goodness-of-fit tests by stochastic simulation

Before conducting a hydrological frequency analysis the best-fit distribution for the hydrological variable of interest must be decided by a goodness-of-fit test or other appropriate methods. In recent years the L-moment-ratio diagram has been suggested as a useful tool for discrimination between candidate distributions. However, few research works have been conducted on the effect of sample size on goodness-of-fit test using the L-moment-ratio diagram. In this study, through stochastic simulation, statistical properties of two estimators, namely the probability-weighted-moment estimator and the plotting-position estimator, of the L-skewness and L-kurtosis of the normal and Gumbel distributions are discussed. The joint distribution of the sample L-skewness and L-kurtosis is found to be approximately bivariate normal for larger sample sizes. Consequently, a set of sample-size-dependent 95% acceptance regions for L-moments-based goodness-of-fit tests of the normal and Gumbel distributions was established using stochastic simulation technique. Such acceptance regions were further validated using simulated random samples, with regard to the consistence of the acceptance rate and the desired level of significance, and were found to be applicable for goodness-of-fit tests for random samples of any sample size between 20 and 1000.