73-Statistics of Extremes in Hydrology.

Abstract

The main objections to the use of a pure statistical approach in the analysis of hydrological extremes are small sample size and unknown distribution function. The ML estimates of large quantiles are highly sensitive to the distributional choice, while the power of discrimination procedures is unacceptably low for hydrological sample sizes. The L-moments method seems to be the best for this purpose. Application of heavy-tailed distributions for extremes modelling is discussed. Moreover two-shape parameter distributions, while some of them are heavy-tailed, are proposed. Keeping in mind that the largest sample element is a low quality data, the effect of its omission on the L-moments accuracy of upper quantiles of twoparameter heavy-tailed distribution is examined. Recent developments in the statistics of extremes are primarily related to the maximum likelihood estimation in the presence of covariates. Its present and prospective hydrological applications are discussed with emphasis on non-stationary flood frequency analysis. As an alternative a two level estimation technique is proposed for estimation of non-stationary parameters of the distribution.