The Estimates of the Parameters of Gumbel Distribution and Their Application to the Analysis of the Water Level Data

The current paper fits and analysis, by means of type I extreme value distribution, the historical data, which is constituted of the highest water levels in calendar years in three survey stations of certain river, so as to predict the highest water level in the future. While the procedures of quartiles, maximum-likelihood and probability weighted moments, are engaged to estimate the parameters involved in Gumbel distributions, the statistical behaviors of these three estimate procedures are compared not only theoretically in terms of so-called large sample theory but also in finite sample simulation by Monte-Carlo processes. After got the estimators of the parameters from the data in hand, the curves of the predicted highest water levels in T years in the three survey stations of certain river, which may be used by the government, are presented at the last section of this paper.