The Application Of Entropy Methods In The Parameters Estimation Of Hydrological Probability Distribution

Hydrological frequency analysis is aimed to utilize existing hydrological data to make statistically quantitative prediction between hydrologic design values and return periods. It is also used to determine the hydrological design characteristic value and its distribution, which provides design values for the planning, construction and operation management of water conservancy and hydropower engineering design. This paper summarizes the application of parameter estimation method by entropy principle and applies entropy principle in parameter estimation of hydrological frequency analysis.The research contents of this paper are as follows.(1) Based on Matlab platform, program codes of several methods for estimating parameters of P-III distribution, two-parameters Gamma distribution and Gumbel distribution are developed. These methods are the maximum likelihood method(MLM), the linear moment method(L-M), the maximum entropy method(ME), the Meilin transform method and the cross entropy method.(2) Using the goodness of fit criteria of OLS and AIC, the most suitable parameters can be determined by ME, Meilin transform, CE, MOM, ML and L-M for three different distributions.(3)This study takes annual precipitation data series of 37 stations in Guanzhong plain of Shanxi as the research object. data is typed into Matlab programs after checking, then estimate parameters of precipitation distribution and evaluate the fitting results.(4)Through goodness of fit test and evaluating the advantages and disadvantages of various methods, we get the optimal distributions and parameter estimations, and expect to provide design basis to the planning and design of water conservancy project in Guanzhong plain.Through the study above, we can get several conclusions as follows:(1) The parameter estimating equations of Gamma distribution, Gumbel distribution, and P-III distribution by the maximum entropy and Meilin transform were derived. The results show that equations of two methods are basically the same, and Meilin transform is better because it can effectively simplify the calculation in the derivation process.(2) Using goodness of fit criteria to access fitting effect of each distribution and parameter methods. For the Gamma distribution, they show that CE is better than L-M, L-M is better than MOM, MOM is better than MLM, and MLM is the same as ME. For Gumbel distribution, CE is the best, while MOM is the worst. For P-III distribution, CE and L-M is better, and ML is worst.(3) Applying entropy principle in hydrological frequency parameter estimation is feasible, and good results are obtained in Guanzhong plain of Shanxi province. When Gamma distribution is used, Maximum entropy and Meilin transform is the same and cross entropy is slightly superior to other methods. For Gumbel distribution, Maximum entropy and Meilin transform is the same and cross entropy is slightly inferior to other methods. For P-III distribution, cross entropy is obviously superior to other methods, and Maximum entropy and Meilin transform are to be further studied due to the appearance of outliers.