零阶矩、一阶矩、二阶矩、三阶矩

参考:Moment (mathematics) - Wikipedia

此处截取其中的一段:

In mathematics, a moment is a specific quantitative measure,
used in both mechanics and statistics,
of the shape of a set of points.

If the points represent mass,
then the zeroth moment is the total mass,
the first moment divided by the total mass is the center of mass,
and the second moment is the rotational inertia.

If the points represent probability density,
then the zeroth moment is the total probability (i.e. one),
the first moment is the mean,
the second central moment is the variance,
the third central moment is the skewness,
and the fourth central moment (with normalization and shift) is the kurtosis.

The mathematical concept is closely related to the concept of moment in physics.

个人翻译:

数学上,“矩”是一组点组成的模型的特定的数量测度。
在力学和统计学中都有用到“矩”。

如果这些点代表“质量”,那么:
零阶矩表示所有点的 质量;
一阶矩表示 质心;
二阶矩表示 转动惯量。

如果这些点代表“概率密度”,那么:
零阶矩表示这些点的 总概率(也就是1);
一阶矩表示 期望;
二阶(中心)矩表示 方差;
三阶(中心)矩表示 偏斜度;
四阶(中心)矩表示 峰度;

这个数学上的概念和物理上的“矩”的概念关系密切。

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