The Estimates Of The Parameters Of Gumbel Distribution And Their Application To The Analysis Of The Water Level Data

In this paper, we discussed the procedures of quantiles, maximum-likelihood, probability weighted moments, moments, least square, the best linear unbiased estimate, good linear unbiased estimation, and the best invariant estimate to the parameters of Gumbel distribution, then give out the expectation and variance-covariance respectively. We compared the statistical behavior of these eight estimate procedures not only theoretically but also in the Monte-Carlo simulation.Based on the data recorded of the highest water level in the three survey stations of Huangpu River, we give out the parameters estimates by using the eight estimate procedures mentioned above respectively, then we calculated corresponding values of likelihood and goodness-of-fit. We reach the conclusion that maximum-likelihood method performs better and more stable than the others.The curves of the highest water level in T years in the three survey stations of Huangpu River, which may be useful to the government, are given out at the end of this paper.