数据分布的偏态:测度方法与软件计算

Skewness of Data Distribution:Measurement Methods and Software Calculation

作为统计数据分布非对称程度(包括偏斜方向和偏斜程度)的衡量指标——偏态,文章讨论了其测度方法及其相应的软件计算。对于由EXCEL的“随机数生成器”生成的对称分布的数据A,当新增数据对算术平均数的影响更大时,Pearson偏态测定法、动差法偏态系数这两种方法都能够正确地测度偏态;当新增加的数据对众数的影响更大时,Pearson偏态测定法的偏态判断是错误的,但动差法偏态系数仍能作出正确判断。软件EViews、MATLAB计算的是总体动差法偏态系数,而EXCEL、SPSS计算的是样本动差法偏态系数。

Skewness is a measure of asymmetry of statistical data distribution(including skewness direction and skewness degree).This paper discusses its measurement methods and corresponding software calculation.For the symmetrically distributed data A generated by EXCEL’s“random number generator”,when the new data has greater influence on the arithmetic mean,both Pearson skewness measurement method and skewness coefficient of the method of moments can measure skewness correctly.When the newly added data has greater influence on the mode,the skewness judgment of Pearson skewness measurement method is wrong,but the skewness coefficient of the method of moments can still make a correct judgment.EViews and MATLAB calcu-late the total skewness coefficient of the method of moments,while EXCEL and SPSS calculate the sample skewness coefficient of the method of moments.