基于抽样分布理论的P-Ⅲ型分布均值的不确定性分析
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摘要
针对P-Ⅲ型分布参数的不确定性问题,提出了应用抽样分布理论进行研究的方法。引入抽样分布及特征函数的概念,推导了P-Ⅲ型分布样本均值的分布函数,构造辅助随机变量并推导了其分布函数,在总体的离势系数和偏态系数已知情况下,结合上下概率分位点得到了总体均值的置信区间;方法应用于上犹江流域,计算得到了其设计洪峰的置信区间。理论推导表明,样本均值和辅助随机变量仍服从P-Ⅲ型分布,且辅助随机变量的分布参数仅与总体的离势系数和偏态系数有关。将该方法应用于上犹江流域,设计洪峰的置信区间合理,说明基于抽样分布理论研究P-Ⅲ型分布均值的不确定性是可行的,且分析结果受总体离势系数影响较大而受偏态系数影响较小。
In view of the uncertainty of P-Ⅲ distribution parameters,a method based on sampling distribution theory is proposed. Firstly,with the concept of sampling distribution and characteristic function,the sample mean distribution function is deduced. And then,an auxiliary random variable is constructed with its distribution function deduced. Then,the confidence interval of population mean is obtained by combining the upper and lower probability points in the case of the known variation coefficient and the known skewness coefficient. The method is applied to Shangyoujiang Basin, and the confidence interval of designed flood peak is reasonable. The theoretical deduction shows that the sample mean and the auxiliary random variables still obey the P-Ⅲ distribution,and the distribution parameters of the auxiliary random variables are only related to the variation coefficient and the skewness coefficient,and have nothing to do with the population mean of the whole. The application results show that it is feasible and effective to study the uncertainty of P-Ⅲ distribution population mean based on the sampling distribution theory.
In view of the uncertainty of P-Ⅲ distribution parameters,a method based on sampling distribution theory is proposed. Firstly,with the concept of sampling distribution and characteristic function,the sample mean distribution function is deduced. And then,an auxiliary random variable is constructed with its distribution function deduced. Then,the confidence interval of population mean is obtained by combining the upper and lower probability points in the case of the known variation coefficient and the known skewness coefficient. The method is applied to Shangyoujiang Basin, and the confidence interval of designed flood peak is reasonable. The theoretical deduction shows that the sample mean and the auxiliary random variables still obey the P-Ⅲ distribution,and the distribution parameters of the auxiliary random variables are only related to the variation coefficient and the skewness coefficient,and have nothing to do with the population mean of the whole. The application results show that it is feasible and effective to study the uncertainty of P-Ⅲ distribution population mean based on the sampling distribution theory.
引文
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[12]李明亮.基于贝叶斯统计的水文模型不确定性研究[D].北京:清华大学,2012.
[13]张冬冬.洪水频率分析与预报中的不确定性问题研究[D].北京:中国水利水电科学研究院,2015.
[14]RATHUBASAMY M,ADAMOWSKI J,KHOSA R.Multiscale streamflow forecasting using a new Bayesian Model Average based ensemble multi-wavelet Volterra nonlinear method[J].Journal of Hydrology,2013,507(25):186-200.
[15]黄振平.水文统计学[M].南京:河海大学出版社,2003.
[16]潘汉臣.上犹江水库的洪水复核[J].大坝与安全,1990(21):33-38.
[2]BENJAMIN J R,CORNELL C A.Probability,Statistics and Decision for Civil Engineers[M].New York:Mc Graw-Hill,1970.
[3]陈璐,卢韦伟,周建中,等.水文预报不确定性对水库防洪调度的影响分析[J].水利学报,2016,47(1):77-84.
[4]雷冠军.P-Ⅲ型曲线参数优选及其不确定性研究[D].郑州:华北水利水电大学,2016.
[5]GOSLING S N,BRETHERTON D,HAINES K,et al.Global hydrology modelling and uncertainty:running multiple ensembles with a campus grid[J].Philosophical Transactions Mathematical Physical&Engineering Sciences,2010,368(1926):4005-4021.
[6]LI B,LIANG Z,ZHANG J,et al.Risk analysis of reservoir flood routing calculation based on inflow forecast uncertainty[J].Water,doi:10.3390/w8110486.
[7]WOOD E F,RODRIGUEZ-ITURBE I.Bayesian inference and decision making for extreme hydrologic events[J].Water Resources Research,1975,11(4):533-542.
[8]刘攀,郭生练,田向荣,等.基于贝叶斯理论的水文频率线型选择与综合[J].武汉大学学报(工学版),2005,38(5):36-40.
[9]梁忠民,李彬权,余钟波,等.基于贝叶斯理论的TOPMODEL参数不确定性分析[J].河海大学学报(自然科学版),2009,37(2):129-132.
[10]梁忠民,戴荣,李彬权.基于贝叶斯理论的水文不确定性分析研究进展[J].水科学进展,2010,21(2):274-281.
[11]梁忠民,李磊,王军,等.考虑参数和线型不确定性的水文设计值估计的贝叶斯方法[J].天津大学学报(自然科学与工程技术版),2010,43(5):379-384.
[12]李明亮.基于贝叶斯统计的水文模型不确定性研究[D].北京:清华大学,2012.
[13]张冬冬.洪水频率分析与预报中的不确定性问题研究[D].北京:中国水利水电科学研究院,2015.
[14]RATHUBASAMY M,ADAMOWSKI J,KHOSA R.Multiscale streamflow forecasting using a new Bayesian Model Average based ensemble multi-wavelet Volterra nonlinear method[J].Journal of Hydrology,2013,507(25):186-200.
[15]黄振平.水文统计学[M].南京:河海大学出版社,2003.
[16]潘汉臣.上犹江水库的洪水复核[J].大坝与安全,1990(21):33-38.
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