P-Ⅲ型分布序列无偏绘点位置计算研究

摘要

[Objective] This study investigated unbiased plotting position formula for Pearson type-Ⅲ distribution.[Method] Expected values of order statistics and double exponential transform method for numerical integration were used to calculate the numerical value of plotting positions for Pearson type-Ⅲ.Then,linear regression was used to develop an approximate unbiased plotting position formula.The derived formula and existing formulas using Monte Carlo experiment were also compared.[Result] Numerical solutions of plotting positions of Pearson type-Ⅲ distribution can be calculated using the double exponential transform method for numerical integration.The unbiased plotting position formula was examined to be highly descriptive and predictive through statistical tests.Under the two evaluation criteria of PPCC and RMSE,annual precipitation data from 36 stations in Guanzhong was chosen for frequency calculation and the goodness of fit was evaluated.The best formula fitting stations were 72.2％ and 69.4％ out of the total stations,respectively.[Conclusion] The developed formula can be applied to hydrological frequency analysis of precipitation data in Guanzhong with good fitting.%[目的]研究P-Ⅲ型分布序列无偏绘点位置计算公式.[方法]应用次序统计量数学期望值原理、双指数变换数值积分方法,求解P-Ⅲ型分布绘点位置的数值解.在此基础上采用线性回归法概化出近似无偏绘点位置公式,并通过蒙特卡洛统计试验将文中近似无偏绘点位置公式与现有绘点位置公式的计算结果进行比较.[结果]用双指数变换数值积分可计算出P-Ⅲ型分布任意绘点位置的高精度数值解.由此推导的近似无偏绘点位置公式具有较好的描述能力和预测能力.在陕西关中地区36个测站年降水数据频率计算和拟合优度评估中的应用表明,在概率点据相关系数、均方根误差2种评价标准下,推导公式拟合最优站数分别占总站数的72.2％和69.4％.[结论]文中近似无偏绘点位置公式可应用于陕西关中地区降水频率的计算,且拟合度较好.