Similarities and differences of hydrologic frequency distribution models and their parameter estimation problems

The consensus since 1950s on the similarities and differences of hydrologic frequency distribution models is reviewed.The similarities and differences of statistical characteristics in these models are analyzed.Under the condition of having the same distribution of geometric shapes,the currently used models with only 3 parameters are essentially different.Observations and real case studies reveal that a unique solution might be existed if a 4-parameter model is considered.We have obtained a unique solution in model parameter estimation using mathematic methods.However,as discussed in the paper,most others first calculate the parameter C_S value that is subjected to larger uncertainty and the C_S value is then used in the calculation of other one or two parameters,which also contain larger uncertainty.As such,the results can only be taken as the initial estimation of model parameters.The rational analysis must be used to finalize the model parameters.