CentralMoment

CentralMoment[list,r]
gives the r^(th) central moment of the elements in list with respect to their mean.

CentralMoment[dist,r]
gives the r^(th) central moment of the symbolic distribution dist.

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

ExamplesExamplesopen allclose all

Basic Examples  (2)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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Introduced in 2007
(6.0)
| Updated in 2010
(8.0)