收入分布曲线的线性正态插值函数拟合方法

The Fitting Method of Linear Normal Interpolation Function for Income Distribution

用样本数据的分组均值与总体方差为参数的正态函数作为插值基函数,构造出线性正态插值函数曲线以拟合中国城乡居民收入的概率分布函数曲线,并论证了这样构造的线性正态插值函数存在且唯一,此插值函数任意阶可微.利用拟合的正态插值函数曲线计算出拟合的函数面积估计值并与相应的样本数据直方图面积做比较,进而得出正态插值函数拟合曲线面积与样本数据直方图的面积误差比率.

We constructed a linear normal interpolation function to fit the income probability function curve of rural Chi na. This parametric interpolation basis function is based on the group means and population variance of the original sample data. We proved that the linear normal interpolation function should exist and be unique, if the group means and population variance of the sample data are the parametric normal interpolation based function. In addition, this interpolation function is the ar- bitrary order smoothness. We compared the estimated area between the fitted normal interpolation function and the corresponding histogram of the sample data, and the result shows that the area error ratio of normal interpolation function curve and the histogram of sample data are small.