Study On Generalized Pareto Distribution And Its Application On Frequency Analysis Of Hydrology

The storm rain and flood frequency analysis approach commonly used in China is the annual maximum series method, that is, only the maximum value in one year is taken as the sample to be analyzed. This way of selecting samples ignores all the others, including the relatively large ones, even though the second one in some year may be larger then the first one of another year. On the other hand, the annual maximum series method may result in a small sample size, which may incur large sampling errors.The partial duration series method can make the full use of the observed information. In this paper, attempts are made to use the generalized Pareto distribution to describe the probability distribution of the partial duration series. The main statistical features of the function, the matrix and the parameters of the generalized Pareto distribution are described and two important behaviors have been justified. Statistical simulations have been done on two parameter estimation approaches, namely, the matrix method and the probability weight matrix method by using the Monte Carlo method. And the results show that the probability weight matrix method has a good non-deviation behavior for the generalized Pareto distribution. Comparison has been done about the sample selecting of the partial duration series method and the annual maximum series method by using the statistical simulations. The effect of different threshold values on the frequency analysis results has been studied.The generalized Pareto distribution has been use to fit the observed data series in Fujian Province. It is seen from the fitting results between the frequency distribution curve and the empirical distribution dots that it is proper to use the generalized Pareto distribution to describe the probability distribution of the partial duration series. On basis of observed partial duration series, the changes of the designed values and the parameter values with the different threshold values have been explored. Initial study has been done on how to select the threshold values.