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

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-Ⅲdistribution 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-Ⅲdistribution,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-Ⅲdistribution population mean based on the sampling distribution theory.