文章摘要
刘可新,胡宇丰,李匡,刘鹏,梁犁丽.基于抽样分布理论的P-Ⅲ型分布均值的不确定性分析[J].水利学报,2019,50(4):420-427
基于抽样分布理论的P-Ⅲ型分布均值的不确定性分析
Uncertainty analysis of P-Ⅲ distribution population mean based on sampling distribution theory
投稿时间:2018-06-26  
DOI:10.13243/j.cnki.slxb.20180594
中文关键词: 抽样分布  P-Ⅲ型分布  不确定性  样本均值  总体均值
英文关键词: sampling distribution  P-Ⅲ distribution  uncertainty  sample mean  population mean
基金项目:中国水利水电科学研究院基本科研业务费专项(AU0145B202019)
作者单位
刘可新 中国水利水电科学研究院 北京中水科水电科技开发有限公司, 北京 100038 
胡宇丰 中国水利水电科学研究院 北京中水科水电科技开发有限公司, 北京 100038 
李匡 中国水利水电科学研究院 北京中水科水电科技开发有限公司, 北京 100038 
刘鹏 河南黄河水文勘测设计院, 河南 郑州 450000 
梁犁丽 中国水利水电科学研究院 北京中水科水电科技开发有限公司, 北京 100038 
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中文摘要:
      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。
英文摘要:
      In view of the uncertainty of P-Ⅲ distribution parameters,a method based on sampling distribu-tion 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 combin-ing 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 de-signed flood peak is reasonable. The theoretical deduction shows that the sample mean and the auxiliary ran-dom variables still obey the P-Ⅲ distribution, and the distribution parameters of the auxiliary random vari-ables 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.
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