Abstract: Taking Gumbel distribution as an example,it is demonstrated in this paper that the influence of sampling errors on the estimation of distributional paramieters can be minimized if using the method of maximum likelihood, and the instability of extremal statistics is mainly caused by the isoiated maximum in the series of eatremal samples.The further research shows that the isolated maximum come from other statistical parent, being the multiparent phenomenon in the eatremal samples, The statistical stability can be maximized if the scarce extrema including these isolated maxima are counted statistically as the regional extrema, In order to meet the needs of engineering design, the probabilities of regional extrema occurred in every stations are calculated.