Dispersion measures for flood frequency analysis

Maximum Likelihood (ML) estimate of upper quantiles looses its optimal properties if a wrong distribution is assumed. Since the estimation is based on the main probability mass, alternative estimation techniques yielding estimates more dependent on upper tail elements of a sample are of interest in flood frequency analysis (FFA). Several systems of summary statistics have been developed and used for matching the assumed distribution to the data. The second LHη = 1 moment is a subject of investigation in respect to mutual relationships with three other dispersion measures, i.e., the standard deviation, the second L-moment, and the mean deviation about the mean value. Using the Monte-Carlo simulations the sampling properties of the four dispersion measures have been investigated. Since the largest sample elements are often low quality data, the robustness of the dispersion measures to outliers is compared. An impact of the system of summary statistics on large quantile estimates is shown as well. The estimation method based on the mean deviation has been extended to cover three-parameter distributions. Real data case study serves to illustrate application of various summary statistics systems for upper quantile estimation.