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零階矩、一階矩、二階矩、三階矩

此處擷取其中的一段:

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.

個人翻譯:

數學上,“矩”是一組點組成的模型的特定的數量測度。
在力學和統計學中都有用到“矩”。

如果這些點代表“質量”,那麼:
零階矩表示所有點的 質量;
一階矩表示 質心;
二階矩表示 轉動慣量。

如果這些點代表“概率密度”,那麼:
零階矩表示這些點的 總概率(也就是1);
一階矩表示 期望;
二階(中心)矩表示 方差;
三階(中心)矩表示 偏斜度;
四階(中心)矩表示 峰度;

這個數學上的概念和物理上的“矩”的概念關係密切。