长江科学院院报
長江科學院院報
장강과학원원보
JOURNAL OF YANGTZE RIVER SCIENTIFIC RESEARCH INSTITUTE
2015年
6期
116-119,126
,共5页
水文频率%负偏序列%极大似然估计%皮尔逊Ⅲ型曲线%MATLAB软件
水文頻率%負偏序列%極大似然估計%皮爾遜Ⅲ型麯線%MATLAB軟件
수문빈솔%부편서렬%겁대사연고계%피이손Ⅲ형곡선%MATLAB연건
hydrological frequency%negative-skewness series%MLE%Pearson-Ⅲ frequency curve%MATLAB soft-ware
针对皮尔逊Ⅲ型曲线参数估计方法中尺度参数β>0,无法适用于潮位、水位等负偏水文序列(β<0)参数估计的问题,从正偏序列与负偏序列的关系出发,提出了一种极大似然估计的新方法。该方法是将负偏序列先后转换为正偏序列、伽马分布序列,并利用负偏序列确定ξ初值,通过伽马分布序列迭代计算得到α,β的极大似然估计值。以某潮位站44 a的最高潮位数据为算例,比较了负偏极大似然法、负偏矩法、正偏查表法3种估计方法对负偏序列拟合的精度,结果发现负偏极大似然估计法的3项拟合指标:PPCC检验值为0.993,OLS检验值为0.010,KS检验值为0.052,均优于负偏矩法、正偏查表法。为此,负偏极大似然法对负偏序列拟合的精度为最优。
針對皮爾遜Ⅲ型麯線參數估計方法中呎度參數β>0,無法適用于潮位、水位等負偏水文序列(β<0)參數估計的問題,從正偏序列與負偏序列的關繫齣髮,提齣瞭一種極大似然估計的新方法。該方法是將負偏序列先後轉換為正偏序列、伽馬分佈序列,併利用負偏序列確定ξ初值,通過伽馬分佈序列迭代計算得到α,β的極大似然估計值。以某潮位站44 a的最高潮位數據為算例,比較瞭負偏極大似然法、負偏矩法、正偏查錶法3種估計方法對負偏序列擬閤的精度,結果髮現負偏極大似然估計法的3項擬閤指標:PPCC檢驗值為0.993,OLS檢驗值為0.010,KS檢驗值為0.052,均優于負偏矩法、正偏查錶法。為此,負偏極大似然法對負偏序列擬閤的精度為最優。
침대피이손Ⅲ형곡선삼수고계방법중척도삼수β>0,무법괄용우조위、수위등부편수문서렬(β<0)삼수고계적문제,종정편서렬여부편서렬적관계출발,제출료일충겁대사연고계적신방법。해방법시장부편서렬선후전환위정편서렬、가마분포서렬,병이용부편서렬학정ξ초치,통과가마분포서렬질대계산득도α,β적겁대사연고계치。이모조위참44 a적최고조위수거위산례,비교료부편겁대사연법、부편구법、정편사표법3충고계방법대부편서렬의합적정도,결과발현부편겁대사연고계법적3항의합지표:PPCC검험치위0.993,OLS검험치위0.010,KS검험치위0.052,균우우부편구법、정편사표법。위차,부편겁대사연법대부편서렬의합적정도위최우。
The commonly used probability density function of Pearson-III distribution is invalid for negative-skew-ness water level and tide level series (β<0).To solve this problem,a means of maximum likelihood estimation (MLE)based on the relationship between negative-skewness series and positive-skewness series is proposed.In this method negative-skewness Pearson-Ⅲ distribution is translated into positive-skewness Pearson-Ⅲ and gamma distribution in sequence.The initial value ofξis decided by the negative-skewness distribution and the MLE ofαand βare calculated through the gamma distribution.In the iterative process the sampling error with evaluating co-efficient of skewness will be avoided.Moreover,the 44-year record of maximum tide level at a tide station is used as calculation example.The fitting accuracy of negative-skewness MLE,negative-skewness moment method and positive-skewness table look-up are compared.The fitting results of negative-skewness MLE (test value of PPCC is 0.993,OLS 0.010,and KS 0.052)are superior to those of the other two methods.In conclusion,negative-skew-ness MLE has the optimum fitting accuracy for negative-skewness hydrological series.