Research On Hydrological Frequency Calculation Based On Johnson Distribution System

The four-parameter Johnson distribution family function(Johnson distribution for short)was proposed in 1949,and it contains three normal transformation forms.The distribution has multi-parameter and multi-type characteristics,and the overall distribution characteristics can be inferred and expressed by fitting samples.The Johnson distribution is a non-parametric statistical method with the characteristics of a parametric method.Its basic principle is to determine the selection of the Johnson distribution family function transformation form through the statistical characteristics of the measured skew data,solve the parameters through the parameter estimation method,and deduce the value of a given design frequency The design value(quantile)of the standard normal distribution is used to reverse the design value of the frequency corresponding to the original distribution through the inverse transformation of the Johnson distribution.Johnson distribution has strong fitting ability.For the standard continuous distribution model,the model can be approximated by adjusting the parameters and selecting the appropriate type.The four parameters of the four-parameter Johnson distribution not only endow the distribution with flexible statistical characteristics and powerful versatility,but also bring many difficulties to parameter estimation.The parameter estimation methods of the four-parameter Johnson distribution include moment method,quantile method,maximum likelihood method and least square method.At present,in the field of hydrology,my country has rarely discussed the application of this model.Therefore,carrying out hydrological frequency calculation research based on Johnson distribution and studying the universal applicability of this model in my country has significant scientific significance and application value for enriching hydrological statistics theory and providing basis for water resources planning and evaluation in the study area.In view of the Johnson distribution has a variety of transformation forms,it can achieve a good curve fitting ability through complex transformation curves.This article discusses five Johnson distribution parameter estimation methods: moment method,quantile method,ordinary least square method(OLS),weighted least square method(WLS)and diagonal weighted least square method(DWLS),and compares Johnson distribution with P-Ⅲ The fit line fitting effect of the distribution is compared.Select precipitation data from 35 meteorological stations in Shaanxi and Ningxia,runoff data from 8 hydrological stations in the Yellow River Basin,and flood data from 10 hydrological stations such as Xiaolangdi and Sanmenxia.Selecting Johnson distribution,and applying 5 parameter estimation methods to study hydrometeorology in the study area.The frequency curve parameters of the sequence are estimated.A comprehensive comparison between the estimation methods of various parameters and the fitting effect of the current P-Ⅲ distribution,the study has reached the following conclusions:(1)The four-parameter Johnson distribution characteristics are studied.The parameterγ can be used to describe the asymmetry of the distribution,and the parameter δ can be used to describe the characteristics of the peak shape of the distribution density curve.The method of moment and quantile are introduced in detail.The principle of parameter estimation method,on the basis of OLS,introduces the nonlinear weighted least square method.(2)According to the five parameter estimation methods of the four-parameter Johnson distribution,the fitting situation of precipitation,runoff and flood sequence in the study area was evaluated.The fitting results show that in the analysis of precipitation,runoff and flood peak sequence frequency,the DWLS method has the best fitting effect,followed by the moment method,OLS method,WLS method and quantile method.(3)Under the five parameter estimation methods of Johnson distribution,through the evaluation of goodness of fit,a quantitative evaluation of the fitting situation of precipitation,runoff and flood sequence is made.The analysis results show that Johnson distribution is generally better than P-Ⅲ distribution.(4)Integrating 5 parameter estimation methods and goodness of fit evaluation,Johnson distribution can be used for frequency calculation of hydrological series,and has good universality and fitting effect.Although it contains some complex parameter calculations,it can be used Computer programming realizes hydrological frequency calculation,so Johnson distribution is also an optional line type for hydrological frequency.