Abstract: Linear moment is one of the important methods to estimate the extreme value distribution function in engineering practice. In order to improve the estimation performance for Gumbel distribution, the estimating results of twelve empirical distribution functions were simulated by using Monte Carlo method. The optimal linear moment estimation method was constructed based on the empirical distribution function with the minimum estimation error, and compared with ordinary moment, traditional linear moment and maximum likelihood method. The study shows that choosing an appropriate empirical distribution function can enhance the estimation accuracy. The optimal empirical distribution function varies depending on the sample size, and its result is quite satisfactory in most cases and offers the best among the other methods especially in the sample size of 1 000~10 000.

Key words: Gumbel distribution, Monte Carlo simulation, empirical distribution function, optimal linear moment, sample size