How to call $\mathrm{Cov}(X,Y,Z)$?

Asked Dec 24 '22 at 18:35

Active Dec 24 '22 at 18:35

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Let

$$\mathrm{Cov}(X,Y,Z) = \mathrm E[(X-\mathrm E(X))(Y-\mathrm E(Y))(Z-\mathrm E(Z))]$$

This can be regarded as a generalization of covariance to three random variables.

I am writing a text where I need to use this quantity, but I have not encountered it in the literature, so I'm not sure if there is a standard name for it. Here are some possible names I think I could use:

Covariance (can be confused with the normal two-variable covariance).
Third-order covariance (not sure about this one).
Third-order centered moment (this is accurate, but I'd prefer to find something shorter).

asked Dec 24 '22 at 18:35

a06e

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That's not covariance. It's coskewness. It's a 3rd moment. The single random variable concept is skewness. – Matthew Gunn Dec 24 '22 at 18:50
@MatthewGunn Thanks, according to that wikipedia page, it can also be called "third cross central moment". – a06e Dec 24 '22 at 22:49
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It is a third central (multivariate) moment. – whuber Dec 25 '22 at 06:10

How to call $\mathrm{Cov}(X,Y,Z)$?

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