Frequency Eatimation For Hydrological Samples With Zero Values

Due to the influence of natural conditions,historical factors,the collection and processing of hydrological data,the hydrological data will be zero or missing.This paper presents a study on frequency analysis methods of hydrological samples with zero values.Based on the current status of hydrological frequency calculation for common samples and the samples with zeros,the paper summarizes the existing problems in the current research.Then the main contents are determined:(1)Based on the total probability theory,the formulas of different probability density functions and parameter estimation methods are deduced;(2)The similarities and differences between the censored samples and the hydrological samples with zero values are analyzed,and the formulas of Partial L-moment are derived;(3)Monthly precipitation data series in the low water period of 42 stations in Guanzhong aera of Shaanxi are used to conduct the frequency calculation of hydrological samples with zero values.The fitting error(?),OLS criterion,and the Akaike information criterion(AIC)are applied to evaluate the fitting effects,and the advantages and disadvantages of each method are analyzed.The main conclusions are listed shown as follows:(1)For the total probability theory,the probability density function which fits the positive values in the sample should be continuous in the range),0(? with a lower bound of zero value.The total probability theory and the order statistics probabilistic have the same plotting position formula.Based on the total probability theory,the Gamma distribution,Weibull distribution and two-parameter generalized Pareto distribution are selected to build the probability density function of full series.Then the related parameters are estimated,and the relationship between the nonzero samples and the total samples are discussed.The results show that the MLM and POME of full series are same with the nonzero values.Some conversion relationship exists between the nonzero values and full series for MOM and PWM.(2)According to the similarities and differences between the censored sample and the hydrological samples with zeros,the hydrological samples with zeros can be considered as a special case where censored threshold is zero.Based on the censored sample calculation theory,partial L-moments formula of the Gamma distribution and the Weibull distribution are derived,forming a theoretical basis for the frequency analysis of hydrological samples with zeros and the censored samples.(3)Based on the total probability theory,the monthly precipitation sequence in the low water period of the study area are fitted and analyzed.For the three probability density functions,the fitting effects show that the MLM and POME of Gamma distribution are better than the MOM and PWM,and the MLM is superiorer than the MOM and POME for Weibull distribution and the two-parameter generalized Pareto distribution.The comprehensive analysis shows that the MLM of Weibull distribution has the best fitting effect under the ? criteria of the high tail.For the OLS and AIC criteria,the MLM of the two parameter generalized Pareto distribution is the best.(4)For the partial L-moments theory,the GEV distribution has the best fitting effect under the criteria of the ?,OLS and AIC.(5)Compared and analyzed the fitting effects of the total probability theory and partial L-moments theory comprehensively,the results show that both theories can be applied to frequency analysis of hydrological samples with zero values.Under the criteria of the ?,OLS and AIC,the partial L-moments of GEV distribution gives the best fit to the hydrological samples with zero values.