BUILT-IN MATHEMATICA SYMBOL

# 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 symbolic distribution dist.

represents the r formal central moment.

## DetailsDetails

• CentralMoment is also known as a moment about the mean.
• CentralMoment handles both numerical and symbolic data.
• For the list , the central moment is given by , where is the mean of the list.
• CentralMoment[{{x1, y1, ...}, ..., {xn, yn, ...}}, {rx, ry, ...}] gives .
• CentralMoment works with SparseArray objects.
• For a symbolic distribution dist, the rcentral moment is given by Expectation[(x-Mean[dist])r, xdist].
• For a multivariate symbolic distribution dist, the central moment is given by Expectation[(x1-1)r1(x2-2)r2, {x1, x2, ...}dist] and {1, 2, ...}==Mean[dist].
• can be used in functions such as MomentConvert and MomentEvaluate, etc.

## ExamplesExamplesopen allclose all

### Basic Examples (5)Basic Examples (5)

Compute central moments from data:

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Use symbolic data:

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Compute the second central moment of a continuous univariate distribution:

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The central moment of a discrete univariate distribution:

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The central moment of a multivariate distribution:

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Find the relation of a formal central moment to cumulants:

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Evaluate for a particular distribution:

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