标准差和平均差的内在关系及应用研究

Standard deviation and the inherent relation of mean differences and application study

由于绝对值不是变量的解析函数,不具有方差的良好数学性质;但由于它对极少数极端事件不敏感,因而更具有抗干扰性。在实证研究波动时,更偏向于平均差。本文正是在此矛盾的基础上,通过考虑分布和不考虑分布的两种情况,从理论和应用的不同角度,深入地研究了两者间的内在关系及应用情况,从而为科学合理地利用离散度指标提供新思路。

Because absolute value is not the analytic function of the variable,the good mathematics nature not with variance; But because it is not sensitive to a few extreme incidents, have anti-interference even more. When the positive research fluctuates, agree more on in the mean difference even more. This text just on the basis of this contradiction, Divide and consider distributing and not considering being distributed two kinds of situations. From the theory and different angles used, each has studied the inherent relation between the two and use the situation deeply. Thus offer the new train of thought for utilizing the dispersed degree of indexes scientifically and rationally.