Moment

Moment[list,r]

gives the r sample moment of the elements in list.

Moment[dist,r]

gives the r moment of the distribution dist.

Moment[,{r1,r2,}]

gives the {r1,r2,} multivariate moment.

Moment[r]

represents the r formal moment.

Details

• Moment is also known as a raw moment.
• Moment handles both numerical and symbolic data.
• For the list {x1,x2,,xn}, the r moment is given by .
• Moment[{{x1,y1,},,{xn,yn,}},{rx,ry,}] gives .
• Moment works with SparseArray objects.
• For a distribution dist, the r moment is given by Expectation[xr,xdist].
• For a multivariate distribution dist, the {r1,r2,} moment is given by Expectation[x1r1x2r2,{x1,x2,}dist].
• Moment[r] can be used in functions such as MomentConvert and MomentEvaluate, etc.

Examples

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Basic Examples(2)

Compute moments from data:

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Use symbolic data:

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Compute the second moment of a univariate distribution:

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The moment for a multivariate distribution:

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