误差绝对值的统计特征和应用

The Statistical Characteristic and Application of the Error Absolute Value

在误差服从正态分布的情况下,研究了误差绝对值的分布、数学期望和方差等统计特征,推导了高阶矩的计算公式;给出了利用残差绝对值对正态分布标准差进行估计的简便方法,残差的变异系数和分布情况可用于考察残差是否服从正态分布,利用误差限和误差平均值及正态分布标准差的关系可对模拟模型中的误差进行控制。

Under the condition of the error obeys normal distribution, the statistical characteristics of the error absolute value is studied about its distribution and mathematical expectation and variance, the calculating formula of high order moment is deduced. A simple method is given to estimate the standard deviation of the normal distribution by using residual error absolute value, the variable coefficient and distribution of residual error can be used to test whether the residuals obeys normal distribution, the error of simulation model can be controlled by using the relationship of error limit and error average and the standard deviation of the normal distribution.