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Someone told me that the term "moment" in Statistics comes from Physics. But I fail to understand how it relates to the definition of a moment of a force, which is a measure of its tendency to cause a body to rotate about a specific point or axis.

Update: I missed the original question about moments and was about to delete mine but I didn't for the following reasons:

  1. The accepted answer is very useful and helps me to better understand the analogy with Physics (and may help another OP).
  2. The answer and the comments clarify the idea that the analogy is more about the moment of inertia than of a force.
  3. The answer in the original question is more about the origin of the concept, which is also helpful.
  4. The title of my question is probably easier to understand for a non-native English speaker and may explain why I missed the original post (and which can also be missed by another OP).
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emeryville
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  • Tis from the Bard: Macbeth Act ii Sc 3: "_Who can be wise, amazed, temperate and furious, Loyal and neutral, in a moment?_" – wolfies May 04 '16 at 05:14
  • @wolfies No man – emeryville May 04 '16 at 05:22
  • Glancing through books.google.com, it looks like moment was used in the mechanics going back to [at least the 18th century](https://books.google.com/books?id=i-jmAAAAMAAJ&dq=moment%20mechanics&pg=PP13#v=onepage&q&f=false) while I'm only finding widespread use of the word "moment" in the context of probability starting in the early 20th century? – Matthew Gunn May 04 '16 at 06:02
  • The concept is more like *moment of inertia* – Henry May 04 '16 at 07:33

1 Answers1

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The physical analogue for moments of distributions is not the moment of a force, it is a more generalised concept. The quantity labelled moment of a force is just the first moment of the force. A more intuitive set of moments to consider in relation to probability distributions are the moments of inertia, which describe the distibrution of mass of a body being analysed in terms of its resistance to changes in angular momentum; or moments of area, which are used to analyse the distribution of a body's area in relation to its centroid.

Note that the integrals involved are very similar to those involved in statistical distributions. For example, for moments of area

$$ \int x.dA $$ is the first moment

compared to

$$ \int x^2.dA $$

to give the second moment.

(Source: Hibbeler, R.C, Statics and Mechanics of Materials, 1991)

Robert de Graaf
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