Application And Research On Nonparametric Statistics Theory In Flood Frequency

This thesis is aimed to integrate the theory of nonparametric statistics and that of transference, establish three nonparametric statistical transference models, explore their applicability in analyzing floods frequency, and provide an alternate method to floods frequency analysis. Firstly , the thesis reviews the condition of the application of nonparametric statistics in hydrology and water resources and points out the difference of nonparametric statistics and parameter statistics in calculation method as well as their advantages and disadvantages. Secondly, it suggests integrating the theory of transference and that of nonparametric statistics as its research focus. Thirdly, it establishes nonparametric density transference model, transference regression model, and floods frequency-analyzing model, which are all applicable to floods frequency analysis. Theoretically, it discusses the consistency and asymptotic behavior of nonparametric transference model, introduces the idea and methods of model building in detail and testifies the stability of the models by means of statistical experimentation. The main factor influencing nonparametric kernel estimation accuracy lies in the choice of kernel function and bandwidth especially bandwidth has an enormous influence on the result of kernel estimation. Adopting the method of transformed kernel estimate helps overcome the contradiction of non bias and minimum mean square error requirement and avoid the difficulty in choosing bandwidth. With the help of transference method, a new sample can be made available. For its corresponding function curve is smoother and the gap of the true value of the statistical points is smaller, using more smooth points can avoid making big errors/deviations. And what's more, optimal function is more even and bias is small, as a result, mean square error diminishes by choosing bigger bandwidth Finally, based on curve-fitting method and non-parameter model, analyses and calculations are conducted on the floods frequency of yearly maximum floods peak flow in Yichang Station, Xiaolangdi Station and Qinhe-based Wulongkou Hydrometric Station, the results of which proves the feasibility of the method. In particular, non-parameter transference model has better stability in contrast to the less ideal hydrological data of curve-fitting method.