# CentralMoment

CentralMoment[list,r]

gives the r central moment of the elements in list with respect to their mean.

CentralMoment[dist,r]

gives the r central moment of the distribution dist.

represents the r formal central moment.

# Details

• CentralMoment is also known as a moment about the mean.
• CentralMoment handles both numerical and symbolic data.
• For the list {x1,x2,,xn}, the central moment is given by , where is the mean of the list.
• CentralMoment[{{x1,y1,},,{xn,yn,}},{rx,ry,}] gives .
• For a distribution dist, the rcentral moment is given by Expectation[(x-Mean[dist])r,xdist].
• For a multivariate distribution dist, the {r1,r2,} central moment is given by Expectation[(x1-μ1)r1(x2-μ2)r2,{x1,x2,}dist] and {μ1,μ2,}==Mean[dist].
• can be used in functions such as MomentConvert and MomentEvaluate, etc.

# Examples

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## Basic Examples(2)

Compute central moments from data:

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Use symbolic data:

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Compute the second central moment of a univariate distribution:

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The central moment of a multivariate distribution:

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