一种修改的双权函数法

A Modified Double-Weighted Function Method

将两个负指数型函数之差所构成的函数类取作权函数 .在确定权函数的参数时 ,主要考虑了两个因素 :(a)权函数与样本容量的关系 ,以反映样本信息量大小在选择权函数中的作用 ;(b)对样本系列中排位在中上部的点据给予较大的权重 .对P Ⅲ型总体分布 ,本文提出的权函数能使σ和Cs 的估计由原方法的二阶加权中心矩降低为一阶加权中心矩估计 .统计试验结果表明 ,修改后的双权函数法无偏性方面优于矩法 ,有效性与矩法相当 ;与PWM法的部分结果对比表明 ,两者统计性能接近 .

In this study, a weight function is constructed by the combination of two negative exponential functions, and the parameter determination for the weight function is based on two factors. One is the quantity of sample information; the other is the distribution of more weight to the data at the middle and upper positions in a ranked sample. For the general P-III distribution, the present function may help simplify the estimation of the Coefficient of Variation (CV) and the Coefficient of Skewness (CS) from the second-order and the third-order moments of the conventional method to the first-order moment. The Monte Carlo simulation shows that the present method is better than the Method of Moment (MOM) in unbiasedness, and is generally comparable to MOM in efficiency. A comparison of the present method with the Probability Weighted Moments (PWM) indicates that the two methods are comparable to each other both in unbiasedness and in efficiency for the studied cases.