Evaluation of Load Values Using the Gumbel Model

The paper deals with application of the Gumbel model to evaluation of the environmental loads. According to recommendations of Eurocodes, the conventional method of determining return period and characteristic values of loads utilizes the theory of extremes and implicitly assumes that the cumulative distribution function of the annual or other basic period extremes is the Gumbel distribution. However, the extreme value theory shows that the distribution of extremes asymptotically approaches the Gumbel distribution when the number of independent observations in each observation period from which the maximum is abstracted increases to infinity. Results of calculations based on simulation show that in practice the rate of convergence is very slow and significantly depends on the type of parent results distribution, values of coefficient of variation, and number of observation periods. In this connection, a straightforward purely empirical method based on fitting a curve to the observed extremes is suggested.