Moment (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-13

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Moment_(mathematics)


00:01:12 1 Significance of the moments
00:06:10 1.1 Mean
00:06:34 1.2 Variance
00:07:17 1.3 Normalised moments
00:08:35 1.3.1 Skewness
00:09:30 1.3.2 Kurtosis
00:11:40 1.4 Mixed moments
00:12:00 1.5 Higher moments
00:12:29 1.6 Transformation of center
00:14:08 2 Cumulants
00:16:36 3 Sample moments
00:17:57 4 Problem of moments
00:20:40 5 Partial moments
00:20:55 6 Central moments in metric spaces
00:21:04 7 See also
00:23:14 8 References
00:26:08 9 Further reading



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SUMMARY
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In mathematics, a moment is a specific quantitative measure of the shape of a function. It is used in both mechanics and statistics. If the function represents physical density, 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 function is a probability distribution, 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 standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.
For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution (Hausdorff moment problem).  The same is not true on unbounded intervals (Hamburger moment problem).